A little out of left field, but you've answered a few Disney asks before, so I'll throw this one out there. It's fun to have variety.
In Frozen, what if instead of proposing immediately, Hans held off and played the long game? I get the feeling the fact some nobody prince proposing to her sister who she just met set off Elsa's alarm bells and that's why she wanted to talk to Anna alone.
But, if Hans had taken it slow and steady, would he have gained Elsa's trust enough to try and kill her to take the throne, or would he have screwed up somehow.
The thing is, Arendelle was about to shut the gates again that very evening. Elsa fully intended to close off the palace the second the party guests were gone, and the coronation was over. She had just gotten through this one day because she had no choice, but she had no interest in opening back up the gates and letting people see her potentially freezing everything.
Anna was an unfortunate casualty of this that Elsa didn't seem to know what to do with/realize there was a very large problem, probably because their parents had only just died right before this happened and this wasn't a responsibility that Elsa expected to take on.
People give Anna flack for being told she could leave at any time and then not doing it/choosing to be miserable... but the thing is where was she supposed to go as the princess of a nation? Anna can't just stroll out the door and marry the local ice-maker. That was one of those statements that Elsa blurted out and I think didn't really think through/realize there had been some... issues...
(And Anna and Elsa's parents were so busy dealing with Elsa's powers that Anna got the backseat for her entire childhood.)
But back to why Hans has no time.
The gates have opened this one, single, day, he goes to the coronation and after party and sees that Elsa is made of stone. He is getting absolutely nowhere with her... which is too bad as that would have gotten him to be king. Anna, however, is flirting with an unfounded desperation/no decorum whatsoever and has clearly grown up with 0 supervision and 0 understanding of her position in life and what she's doing.
(It's telling that Anna's growing up montage is just being bored and getting into trouble and... seems to involve no tutoring whatsoever/no contact with anyone. Probably the parents thought that too many outsiders brought in just increases Elsa's risk of an accident--but I get the feeling Anna was taught nothing which is wild even if she wasn't crown princess.)
Hans isn't just the hunky guy Anna met at a party who finishes her sandwiches, he's her chance to get out, to see the world, to live a normal life and talk to people instead of pictures.
Anna's parents are dead, her relationship with her sister is nonexistent/really frosty for reasons she can't explain at all except "dunno, maybe she hates me", everywhere she goes she just causes a mess of things--she's looking at the rest of her life and it is long, bleak, and dark.
Anna would have picked any hot guy who paid attention to her at that party (and the movie does have a good message and all, Anna shouldn't have rushed in without knowing this guy, good message for the kids... but I see how Anna got here and find it a little wild that we give Anna all the flack for that and none to the many environmental factors that led her to this point).
Anyway, Hans sees all this, knows that the Arendelle princesses have been completely isolated since childhood, and I think he sees the writing on the wall.
Chances are, once the party's over and all the dignitaries of foreign nations are sent home, neither Anna nor Elsa will be appearing for diplomatic engagements with other nations. Further, there will be no events in Arendelle for Hans to pop into. No balls, weddings, nothing.
This is the first, and perhaps last, time Hans will ever be in Arendelle.
And so, Hans has got to go for it, Anna's into him, is the most desperate woman he's ever seen, MARRY HIM ANNA AND GET HIM ONE STEP AWAY FROM THE THRONE RATHER THAN FUCKING SEVEN!!!!
In other words, Hans is as desperate as Anna is, but he knows it.
The party continues, Anna spends the entire night flirting with Hans of the Southern Isles with seven older brothers. She's in love! She's so in love! He's so hot! They're so perfect for each other! As a result, Elsa barely sees her sister that night which is... a good thing as well as a bad thing.
Good because things are very awkward between them, Anna doesn't remember that time Elsa accidentally nearly killed her, Anna has no idea she has ice powers, and they haven't actually spoken in years.
Bad because this was Elsa's big chance to connect with her sister (they said a few words about chocolate!) and patch things up now that their parents are gone and they have, well, the rest of their life. But this also would have been a bad idea because close is bad and could lead to icy accidents.
So, Elsa's a little upset, but the worst of the coronation is over and now she just has to get through this fucking party which will wind down sooner or later.
Because Anna doesn't march up to Elsa and announce her engagement on the spot (casting Elsa in the unexpected role of Tevye while she wonders how she briefly wandered into the wrong musical) there's no conflict between them. Anna, for her own party, is so giddy at all of this happening she wouldn't even think to be disappointed he didn't propose to her right then and there. I don't think it'd even occur to her to fantasize about, she had a great time!
The conflict comes after the guests leave... and Elsa promptly shuts the gates.
Anna is dismayed, broken, and angry. The gates are shut?! She had that one day?! ONE DAY?! She bitterly complains to Elsa about this and here I imagine Elsa responds much the way she did in the film, it's her decision and if Anna doesn't like it... she can go leave.
Anna points out that she has met the love of her life tonight. Elsa can't just cut things off before Anna has a chance to see him more than one time. Is Anna supposed to become a nun? Except not because being a nun would require leaving the palace to go live in a convent at least! NUNS ARE GETTING MORE ACTION THAN ANNA.
Elsa's likely a little more sympathetic--but not really. Anna, you're not in love with this man, you just met him and know nothing about him. Calm down.
And I imagine Elsa brings up the "then leave" argument again as it's the only real argument she has without explaining "ice powers" and it's something Anna can't argue with. If Anna's choosing to stay here then she has to play by Elsa's rules, and if she can't, she can walk out those damn gates herself!
"FINE, I WILL LEAVE!" Anna declares, because if that's an option (her only option) then fine. Her sister clearly doesn't give a damn about her whatsoever, her parents are dead, AND SHE IS IN LOVE WITH HANS OF THE SOUTHERN ISLES!
Anna will leave, and go to the Southern Isles, and say "Wow, Hans, funny meeting you here, I love your southern isles, so south, such wow."
Does she know where these islands are? No. Does she have any idea how she would get there? No. Does she have any idea the implications of a princess sending herself to a foreign nation, with no warning, where if this nation isn't friendly is a great opportunity to take her hostage? No. Does she have any idea what saying "Elsa the queen told me to leave" implies/she will essentially be in exile? No.
BUT ANNA IS GOING ANYWAY.
Anna packs very poorly, too giddy about her plan/having no idea how or what to pack/having no idea how far the Southern Isles are or what the climate is there.
I imagine she Kronk-like sneaks out of the castle, despite Elsa having given her permission to go as it still feels forbidden. WOW, SHE IS OUT OF THE CASTLE, WOW! The gates aren't open but she's out of the castle! This is so forbidden and amazing.
NOW TO GET TO SOUTHERN ISLES!
Anna realizes she has no idea how to do that.
Well, islands are in the ocean so she would take... a ship! Depending when Anna snuck out she either goes to the docks to start asking people right away for passage to "The Southern Isles" or she's very sad and confused as... no one is here (because it is the middle of the night).
Those who are captaining small local fishing vessels look at her in disbelief and horror. Lady, do you know what a boat is? Do you know what the ocean is? Do you think this rowboat can handle open water?
Anna is very discouraged by this but is not returning back to the castle!
(Meanwhile, Elsa is in two states: she has not realized Anna has left because their contact with each other is so hilariously bad that she has not realized she is missing, she has realized (likely due to being told by a servant) and is now in angsty icy misery as her sister really took her up on that and abandoned her and oh god Elsa didn't actually mean it and now she's all alone in this castle all by herself and her sister has left her!!! There are likely suggestions that she send the palace guards to go pick up her wayward sister and I imagine Elas is tempted, it's the reasonable thing to do... but she did just tell Anna that she could have left whenever she wanted and boy she'd be eating her words if she brought Anna back now.
"If this is what Anna wants, this is what Anna gets.")
Anna likely eventually finds a trading vessel that does do trade with foreign nations, Southern Isles included, and gets a long hard stare. Either the captain recognizes that she's the princess, and is attempting to run away to another country, in which case they probably don't want anything involved with this because there goes their business and their head. If they don't recognize Anna (she has been cut off in a castle for years) then this is one seriously weird rich (noble???) woman who... wants to charter a course to the fucking Southern Isles, which are far away and... why?
Former case, she gets sent right back to Elsa where the pair have a massive blow up about how Elsa was bluffing about Anna leaving any time she wanted and she's trapped here isn't she! IT WAS ALL A LIE! ANNA ISN'T EVEN SURPRISED ANYMORE.
Elsa... may or may not accidentally unleash her ice powers, in which case Anna gets hit and is in serious trouble with Elsa having to desperately cart her sister to the trolls (and likely unleashes eternal winter as she's so upset while she does this), or Anna doesn't get hit and Elsa likely unleashes eternal winter as her sister has found her out and is not safe around her and SHE'S RUNNING TO THE MOUNTAINS, ANNA.
Latter case, we get Frozen but there's no Hans subplot/the Hans subplot is that Anna met a hot dude at a party and it was so cool but god what the fuck is her sister doing and ANNA IS VERY SORRY BUT WOULD LIKE TO POINT OUT THIS IS MOSTLY NOT HER FAULT.
Former case, Anna and Elsa have a very weird heart to heart after the trolls where Anna learns that Elsa has had magic powers, this whole time, this is the second time Anna's been hit with them and... turned out love was the answer, I guess.
"Can we open up the castle gates?/Can I write Hans?" - Anna
If the captain doesn't recognize Anna... the thing is, Anna looks like trouble. She's horribly clumsy, clearly has 0 idea what she's doing, and while that money is so tempting they'll be on this boat with Anna for some amount of time. And what if she comes back and says "take me back to Arendelle, I changed my mind", so we're still probably back at the "Anna ends up confronting Elsa again.
Does Anna Ever Meet Hans Again?
Honestly, maybe but unlikely.
If Anna and Elsa resolve their differences then Hans was a great guy she met at a party, so hot, but Anna's distracted by hanging out with her sister/having the relationship she always wanted with her. The need to get out of Arendelle isn't nearly as strong, nor is the loneliness.
Hans is still great, love Hans, so hot, so great--but Anna's kind of busy right now and isn't really in a great place for a second major relationship in her life.
I can actually see her sort of forgetting about him, which makes it awkward if/when he shows back up and asks Anna if she remembers the sandwiches. Does she remember the sandwiches?
"... No..." Anna says because wow he is cute but.. hm, she wants to talk to her sister about chocolate, k thanks.
And Hans cries as he hit a dead end and didn't take advantage while he had the chance.
I am reminded that Hans has twelve brothers, not seven, which makes it even worse.