@giltheweebzard replied to your post “Starting the year off right: thinking about...”:
Don't forget Monet incapacitated Robin before she could use her abilities against her. And while Nami could use heat effectively, she and Chopper got bailed out by Zoro who drew attention from Monet.
Monet is definitely one of the most pragmatic characters in the series, which is in turn aided by the fact that she's well aware of where she stands relative to everyone else
She was able to "beat" Luffy because he wasn't getting serious against her; if he'd actually made a real effort to overpower her, he definitely could have, and she acknowledged that, so she made sure to go for a capture rather than for a win while he was still underestimating her
The circumstances of the fight play just as much of a role as the fighters, but let's take a look at how the match-ups might go if everyone were just plopped into battle without any context
Luffy: his Haki and overall strength easily overpower Monet if he's actually making an effort, as we've established
Zoro: same as above, and seen in canon
Nami: her Heat Eggs definitively give her an advantage, and the heat from her lightning attacks should work on Monet as well, but given Monet's speed, she should be capable of maneuvering around Nami's attacks once she knows to be cautious of them. Nami's weather manipulation could likely prevent Monet from conjuring a snowstorm and gaining a field advantage, but that might also just lead to a stalemate. If Nami lands a lightning attack, she wins, but she'd have to really strategize around Monet's abilities. I'm gonna call this one approximately even, but I'll give the advantage to Nami on the basis that weather is her entire thing
Usopp: I don't know how well his Pop Greens would work in a cold environment since they're from a tropical one, so there's a good chance that Monet could make her surroundings too inhospitable for them to be used properly. Usopp has used flame-based attacks before, so he definitely has a way to harm Monet even without Haki, but again, it's a matter of actually hitting her since she's very good at outmaneuvering her enemies. If he ever learns to actually utilize his Observation Haki, he'd probably be able to find where she hides in the snow, but if she's being cautious of long-ranged attacks, she'd probably be able to catch him before he can use his arsenal effectively. Usopp has a way to win, but advantage to Monet
Sanji: in terms of strength, Sanji wins - fire powers, Haki, iron skin, no contest. Buuut it's Sanji. He can't hit her, he won't hit her, he'll let himself die. Best bet is to tag in someone else
Chopper: no Haki, no heat-based abilities; he might be able to concoct a medicine of some kind that would allow him to produce heat, like a reverse version of Queen's Ice Oni, but Chopper's never been shown using medicine offensively aside from the Rumble Ball, so I'm not inclined to believe that he would. Even in Monster Point, Chopper doesn't have a way to hurt Monet and would really only be giving her more surface area to hit, though it might make him durable enough to resist most of her attacks. Monet has the advantage, though it would most likely come down to a battle of attrition more than anything else
Robin: Monet being a Logia-user gives her a distinct advantage, as Robin's grappling techniques are rendered completely moot; Robin's best hope against Monet is to use Fishman Karate, which can damage Devil Fruit-users the same way that Haki does, but Robin has thus far only used Fishman Karate strikes as a set-up for her grappling, so we don't have much reason to believe that she has anything in her arsenal that would allow her to land a definitive blow. If she has more techniques up her sleeve, sure, but as it stands, Monet most likely wins
Franky: Multiple methods of taking advantage of Monet's weakness to heat (fire-breath, laser beams, etc.) and a near-invincible body give Franky the distinct advantage, though Monet's cunning and strategy could eke her out the win. Still, I'm giving this one to Franky since I don't know if Monet's offenses have a way to get around Franky's iron constitution. Edit: Reevaluated this, I forgot that Franky's back is still his weakness post-timeskip. Monet would definitely figure this out since she favors attacking from behind. Franky is also canonically the second-slowest Straw Hat and almost exclusively wins his fights through brute force instead of strategy, so Monet would definitely land her hits with little difficulty. In the worst-case scenario, Monet would likely figure out that she can freeze Franky's cola to render his weapons useless. Monet takes the advantage
Brook: Brook's ice attacks shouldn't have much effect on Monet given that she's already frozen, though it's been stated that Aokiji's ice Logia would overpower her snow Logia the same way that Akainu's lava overpowered Ace's fire, so it's certainly possible that Brook could freeze Monet's snow into solid ice to force her into having a corporeal body, but that depends on how adept he is at using cold, I think. Brook's speed also gives him a good counter to Monet's, but a lack of Haki makes his offensive options a lot more limited. He uses his hypnosis abilities so rarely that it's hard to say whether they would affect Monet, but I'm inclined to believe they wouldn't since he only really uses them on fodder enemies. If ice overpowers snow he has a way to harm her, but being able to harm her isn't the same as being able to beat her. I'm going to give this one to Monet, but cautiously. Edit: after much thought, I've decided that Brook's ice should be able to harm Monet, and his speed should be more than enough to keep up with her, even if only via reaction time. Brook has shown resistance to being frozen (as he has no flesh or blood), and his lack of organs makes him resistant to stabbing attacks. Only Monet's bites pose a real threat, and they're her slowest attacks (Nami could move Chopper out of the way while otherwise immobilized by Monet's cold, which wouldn't affect Brook). This one goes to Brook, but Monet's strategies still give her a decent chance
Jinbe: no contest, Jinbe's on at least Doflamingo's level and is both skilled in Haki and the foremost Fishman Karate master. He's so serious that I don't even see a way that Monet could get the drop on him in any situation, either, but perhaps her binding-based abilities would let her hold her own for a while
So that's three definitive losses (Luffy, Zoro, Jinbe), three solid wins (Usopp, Chopper, Robin), two shaky losses (Nami and Brook), one shaky win (Franky), and one default (Sanji)
Huh, that came out a lot more balanced than I was expecting to be, actually. Basically three each of losses, wins and possible draws. Honestly, though, if Oda put any of the Straw Hats against Monet, he'd probably find a way for them to win, since generally the crew doesn't lose their arc fights, but that should only strengthen the argument that Monet isn't too weak to join. They're all dolls that Oda plays with as he sees fit, he can just write a way to win any given fight. He's skilled enough to do so with logical consistency between battles, but still, if Monet joined, he'd make sure that she's a competent enough fighter to beat whatever opponents he'd have her up against and would make her just as viable a combatant as anyone else on the crew
In short, "too weak to join" is just an excuse that people use to derail the argument
