Upsides of Daemon as the second eldest of Daeron 2's brats:
-dragons before the rebellion
-gets to punch Aegor Rivers in the face at half his size at least once for free
-Aegon 4 having to deal with indisputably legitimate Daeron 2 if for no other reason than because Daemon the Rogue Prince Come Again (with free bonus Caraxes (Caraxes survived and hid in the god's eye island until his best boy came back? with free sword? Caraxes Reborn as cradle egg? some third thing?)) keeps challenging people to trials by combat at pint sized age and keeps winning!!!
-Daemon and Rhaegal mutual gremlin energy
-Daemon getting to punt Other Worse Daemon around the yard
-Daemon getting to explore Dorne! He hates it!!!
-Daemon and Aemon the Dragonknight in the same vicinity
-"six men or sixty, he's still Daemon Targaryen" Redgrass edition
Upsides of Daemon as the second eldest of Baelor Breakspear's brood:
-Even less Valyrian than ever before: panic
-Free excellent parents and older brother in Valarr
-new exciting younger brother!!! they get into SO MANY shenanigans!!
-Daemon the namesake sneaking his tiny ass onto the battlefield at Redgrass for ultimate surprise Caraxes burninating his annoying great uncles
-sooo many bitty cousins looking up to him and following him around oh the anxiety, but also more family!!!
-fun experiment of "how much dragon blood to control dragons" anxiety in his second first marriage, still gets his boys!
-giving Baelor proof that "dragon" is not actually the solution to all problems people (his family) think it is, but it sure helps in some cases
-giving Aegor Bittersteel a jealousy ulcer
-pitting Volantis against Tyrosh in new fun ways by accident
-getting to kick Aerion into the dirt for free
-"six men or sixty, he's still Daemon Targaryen" Ashford Meadow Trial of Seven edition (saving Baelor's life in the process). also prevents the kingsguard from participating since Daemon wouldn't leave it at the last minute. (tiny cheering squad Jon and Rhaegar that Egg has to keep a handle on, much to his dismay)
Silly thoughts silly thoughts
It's strange to think how close in age he is with Daemon Blackfyre here, given that B!Daemon is roughly of an age with Baelor. So you have B!Daemon and then our R!Daemon who is, like, maybe 2 years younger.
But you know, I'm not sure if Daemon being a sword-wielding prodigy is necessarily helping the Daeron "son of Aemon the Dragonknight" allegations, unless it somehow appeals to Aegon's ego. Which, granted, it very well could, given that Daemon is bonded to a dragon! But also, I'm sure that Daemon is super drawn to his great-uncle Aemon, even as he finds certain aspects of Aegon + Naerys + Aemon's history suspiciously familiar, thanks to Rhaegar's Dragonknight stories. So Aegon's gonna be annoyed/frustrated about that at least.
Oh, and the absolute horror of learning that he's his own great-great-grandchild, but not by Jon or Rhaegar, WHO ACCORDING TO HISTORY DON'T EXIST WTF, but some unfamiliar son who was HELD CAPTIVE BY LYS. Poor Daemon isn't going to take a full breath until he finally has his twins someday.
For claiming a dragon, it seems like this was the era of desperately-leveraging-cradle-eggs-in-the-hopes-that-one-will-hatch, so that appeals to me a lot, because suddenly one does! And no one was ready for that! But huge ++++legitimacy for Daeron when it happens. (Pretty sure B!Daemon advocates hard for his own egg out of a natural rivalry with R!Daemon.)
I'm curious what Daemon ultimately ends up feeling about Dorne. I could see a love/hate forming. He stubbornly doesn't want to like it, but he has his mother's spicy palate and loves the food, and the terrain is quite different than what he's used to, which makes it interesting, and maybe he meets a member of House Dayne who reminds him a little of Rhaegar. (House Dayne match for Daemon, perhaps? Just don't steal your younger brother's girl! 😂)
Also, so many very different brothers to form various relationships with. Does Aerys remind him a little of Rhaegar's enthusiasm for books? Does Maekar's frown at times look like Jon's? (Though I'm sure Baelor also reminds him a ton of Jon.)
Uh oh, running out of steam here. I find this slightly less fascinating, just because the previous generation or two is so politically chaotic, while this one involves a lot of people eventually dying off to thin out the family tree a bit for eventual Summerhall. Even so, as you said, still plenty of brothers and cousins underfoot! (No sisters in any of these scenarios. Gotta be a Maekarling for that!)
How obsessed is Aerion when Daemon claims a dragon? What does that do to the poor kid, in fact? I think it's easier to fall into delusions of "I am a dragon" when there are no actual dragons around, but when there is a literal one to behold, surely it becomes "I WANT a dragon?"
Mostly though the appeal of this setup is how many headaches/scares Daemon gives Baelor, given how well-behaved in comparison his brothers are lol. Then there's the awkwardness of his second son being the one with a dragon. And I mentioned before, in this scenario, I think Maekar ends up as the favorite uncle for Daemon, who feels at least a little vindicated to see perfect Baelor have to deal with at least ONE gremlin. Pretty sure he laughs his ass off at the first white hairs that show up on Baelor's dark head.