Perilous Trails is not the best representation for Itto...
Itto is a very hard character to comprehend. The base is simple : a troublemaker with a heart of gold, and while he might be all over the place and a bit too competitive for his own good, he has morals that he strictly sticks to.
But in practice it's actually more complicated to show this balance in him than you might think. You have to make him careless enough so that the 'trouble' and 'himbo' parts of his personality are present, but responsible enough to ensure he respects the "Oni Pride".
He do whatever he wants because of the Oni Pride, he's not going to put on a picture perfect act when it's not who he is. But whatever he wants at the end is fairness, equality and the safety of others. And winning in the process is a pretty big bonus.
And while this quest shows some understanding of Itto, (we all saw him punching the door, i'm not going to pretend like it's not something Itto would do because it is, and it's hella funny.) it also lacks some understanding in the other aspects of this character.
For example when he puts up a fight with Yelan at the beginning of the quest. Yes Yelan is an authority figure in this case, yes Itto doesn't care in the slightest if an authority figure approves his decision or not (unless it's Granny Oni or Kuki Shinobu) and he shows it quite well in his character quest with the Tenryou Commission.
But this is not the same context here. He is in an unknown land, in a unknown place and is trying to keep his "savior" (Yanfei) safe. And a random women who quite seem to know what she's doing tells him that this place is dangerous and he shouldn't stay here.
His morals clearly indicates that he should not back down against injustice. And it's clear in this moment that this is not injustice, Yelan is trying to keep everyone safe, including Yanfei.
So based on everything I said so far, it doesn't make much sense that he would get angry against Yelan. He would bargain, try to convince Yelan that he is capable of surviving down here by proposing a duel or even convince everyone to get out of this place and get to safety, meanwhile he and Yelan will do whatever Yanfei needed to do in her place so that she doesn't have to be in danger.
And I get that they needed to put a fight here so that everyone would get stuck in the timeloop (or timehole, i don't know how to describe it). I get that they needed to have some kind of tension beforehand so that you could clearly see them slowly warming up to each other and forming the best of teams.
But this is exactly where the difficulty of storytelling is. You have a bunch of characters with their own flaws and strengths, you have a situation in which you want to put them in and now you have to use those flaws and strengths to make it work. It's not an easy work, no one said otherwise here.
But the fact that this is complicated doesn't mean you can rough up a character's personality, even just a little, so that everything works. The writers could have added some kind of pre existing tension between Yelan and Kuki, a sort of cold relationship like Diluc and Kaeya. Kuki has been to Liyue, Itto considers Kuki as part of the gang and thus a part of his family, so if Yelan let out some passive aggressive comment about Kuki because of some pre existing tension due to an old event between the two of them, then Itto would get mad.
Then Itto would want to fight her, then the situation goes wrong and boum they are stuck in timeloop/timehole.
Same thing for when Itto decided to knock a wall with all his strength to make the arguing stop. The part that triggers me here is not his sacrifice for the good of others, he is able to do that, it's the fact that he does this without saying anything before hand.
Itto is anything but silent that's for certain. Before doing that he would at least yell a big "shut up" to everyone. Maybe he could yell that, hit the wall and say to or three sentences before fainting, because of course he wouldn't have planned the part where something bad would happen to him. He would have thought that he could still have some force left in him after that, because he is full of hope and would only hope for the best.
But in my opinion having him unconscious for the second half of the quest wasn't the best idea in the first place. Firstly because I absolutely adore him and he is literally my main, so having a quest with him being conscious only half of the time isn't what I can call satisfying.
Secondly because at the end for Xiao's sacrifice, I would have absolutely loved it if Yelan AND Itto were the one to go and get him. I mean the two people who caused this whole thing (not entirely, but if they didn't fought in the first place...). Itto would never want to see someone close to him sacrifice themselves for him, Yelan cannot allow that to happen again.
One of them is spontaneous enough to jump, the other one is protective (and traumatized) enough to jump. I don't see why this didn't happen to be honest.