It's interesting (and important) to point out that arcs where the whole crew got a fight weren't that common Pre-TS either. I think it makes more sense though to also count the arcs where most of the crew got their own fight, too, because otherwise, you actually end up with one single arc in the whole series (Alabasta).
If you count those arcs as well, than you'll find that 1 vs. 1 (or 2. vs. 2 etc.) fights usually only happen in bigger arcs where the Strawhats take on a whole crew of enemies, with several distinct members.
As was pointed out, Arlong Park arc is the first of this kind, which is very fitting, since that one always feels like the arc where the crew truly comes together as a unit for the first time to help Nami.
After that though, we get a whole bunch of smaller arcs that mostly serve to setup the big climax of the saga, the Alabasta arc. In those smaller arcs, it's mostly selected crewmembers who get their own fight, if at all. Even Zoro doesn't really get his own 1 on 1 in Little Garden or Drum Island. Chopper is pretty much the only character besides Luffy to get one in the latter arc.
Alabasta stands out as the one single arc where truly every single member gets an awesome fight, except for Vivi. The 'princess that needs saving' of the arc usually doesn't get their own fight, plus Vivi is only an honorary member of the crew, anyway.
Jaya is a short and sweet arc with not much fighting going on, and then we've got the big Skypia arc. Paraplonq left it out of his list, but if you count arcs where most of the crew get a fight, it should be included, too, because Nami, Chopper and Robin all get their own fights while Zoro even gets two for the price of one here. Sanji and Usopp do have that fight against Satori together with Luffy, one of the rare cases where a couple of Strawhats take on one single enemy (the fight lasts a whole three chapters, too!). I guess it count be counted as half a battle for Sanji at least, since he is the one to take Satori out.
The Davy Back Fight arc focuses more on games than fights, though Sanji and Zoro taking on the Groggy Monsters in a ball game kinda counts as a fight for them. Counting Water 7 and Enies Lobby as one big arc, with Water 7 mostly functioning as the setup and Enies Lobby as the climax, you have Sanji, Zoro and Franky each getting a fight during the Sea Train chase, and then of course the climactic CP9 fights, where everybody from the crew minus Robin and Usopp get their own fight. Robin is the 'princess' character of the arc, so she naturally doesn't get one (though she does take out Spandam at the end). Usopp is a different case. That feels like a very deliberate choice by Oda - Usopp didn't get a fight because the whole point was that Usopp not being a super strong fighter doesn't make him worthless. Thus, the focus was on his sniping skills instead.
Thriller Bark is interesting, because it's one of these 'sort-of big arcs'. It's not a huge climax to anything but it's also not a small arc by any means either. Appropriately, about half the crew get their own 1 vs. 1, namely Usopp (after getting the shaft in Enies Lobby), Sanji and Zoro. I guess you could count Chopper and Robin vs. Hogback and Cindry as a 2 vs. 2, but it feels more like an emotional standoff than anything. It's made pretty clear that they would have defeated them if it hadn't been for Oars intervening though. I always really loved that whole confrontation as a character moment for Chopper btw, I think it's very underrated (as is this whole arc). Oh and then we have that super-awesome fight between Oars and the whole crew, which I love from beginning to end (Can you tell I really love Thriller Bark?
Well, afterwards we don't really get any notable crew fights until Fishman Island. Even though those fights are given a bit less attention, since it's just the New Fishman Pirates they are beating and it's mostly a showcase of the Strawhats power after the TS. Still, almost everybody gets a fight here, except for the girls - well, I guess except for Nami if you count Robin defeating Hammond as a fight. I'm still a little sour that they were shafted like this. Sanji and Jinbe team-up against Wadatsumi, but hey, give them a break, he was like three-times the size of Oars or something. It counts as a fight to me!
Punk Hazard kind of feels to me like the Little Garden of Dressrosa, with the crew taking on a few of the main villains minions before the big, saga-ending arc, though like everything Post-TS, it's on a much larger scale. Still, there are only a few secondary villains in this one. Sanji has a skirmish with Vergo, who than fights Smoker and is ultimately taken out by Law, while Monet fights Zoro but is ultimately taken out by Tashigi, so ehh. Franky gets a sweet little fight against Buffalo and Baby 5 at the end, though.
Dressrosa is an interesting case. I feel like it should count as one of the arcs where (almost) everybody gets a fight, because (almost) every major character who is present at the climax gets their own fight. Almost, because of course, poor Robin gets shafted again. Franky, Zoro and Usopp all get fights though (yes, I count Usopp sniping Sugar as a fight - it's how a sniper fights, after all), as do all of the major Colosseum fighters (who sort of function like a substitute crew in this arc to me) and Kyros.
Nobody gets a fight in Zou and then we are already at Whole Cake Island, and I feel like this arc is the reason a lot of people fear that the Strawhats might not get any actual fights in Wano, or that their fights might be off-screened. Oda has been very consistent about giving most of the crew a fight in big arcs so far, and that includes Post-Timeskip, but this arc is the big exception. Luffy gets two 1 on 1's here, while nobody else does and it's certainly not a small arc. But then again, this arc is probably one of Oda's most unusual arcs in the series anyway. The Big Bad doesn't get defeated at the end (and the goal is never to defeat her or her crew, to begin with) and appropriately, the arc ends in a (untypically for One Piece) bittersweet fashion. And while it's true that the other present crewmembers don't get a true 1 vs 1 fight, they all get plenty of screentime and tons of cool or memorable moments. It's not like Oda was sidelining them in this arc. Sanji not getting a fight feels very reminiscent of Usopp not getting one in Enies Lobby - like a very deliberate choice by Oda. This arc wasn't about Sanji showcasing his superior fighting skills to his brothers - because, to me at least, Sanji had nothing to prove here, I always felt completely sure that he could beat every single one of them 1 on 1. It was about Sanji showcasing his actually important skill, the one that truly marks his role on the crew, the one that Sanji's father is unable to comprehend or appreciate: his cooking.
So (very) long story short, Oda has been very consistent about giving most of the crew a fight in big (or bigger) arcs, with Whole Cake Island being the sole exception as a very exceptional arc in general. Wano is a lot more consistent with our typical arc structure in One Piece, though: Our main goal is to defeat the big villain and his minions and free the country. The Strawhats are setup to do just that. Oda would truly break his pattern here if those fights were mostly or completely off-screened. Let's hope he doesn't because I'm more than ready for the crew to kick some ass