what evidence do you have that bj and hawkeye are only friends because they are "trapped in an army base" and "hawkeye doesn't have any better options"?
tbf I didn't say they're only friends because they're trapped on an army base, I said BJ only gets away with his late season shit because they're trapped on an army base. That said, I do think if they'd met anywhere else, like at a medical conference, they wouldn't have become friends, and yeah the way they clash in the later seasons, I don't think they'd stay friends if Hawkeye wasn't stuck with him.
My evidence is:
Hawkeye describing BJ as a good clean-cut family man and adding "Despite that, I really like the guy," in Our Finest Hour, indicating that on a surface level they're not that compatible. On a deeper level of incompatibility, you have episodes like Preventative Medicine where they clash on a deep ethical level and don't reconcile their points, they simply choose to drop the argument. You also have their respective attitudes to hardship as highlighted in later seasons - BJ "saves [his] pshaws for things he can do something about," and largely remains passive give or take moments of sudden lashing out (eg the end of Back Pay) when he loses his self control, while Hawkeye is always acting on his feelings as much as possible whether he can affect change or not, because it helps him not feel helpless. BJ derides and mocks this attitude (calling him crazy in Back Pay and Tell it To the Marines, calling his tongue depressor tower pointless in Depressing News, etc) and Hawkeye ignores him and does what he needs to do anyway. They do not help each other see eye to eye or meet in the middle, they simply clash and do their own thing.
More headcanony, but I also think they're incompatible emotionally, in that Hawkeye wants people to open up to him and spill their feelings, and BJ is one of the characters most allergic to doing that, and almost never supports Hawkeye when he wants to talk about his feelings (Blood and Guts, Depressing News, GFA, etc). They have a very uneven relationship where Hawkeye is BJ's emotional support whenever BJ snaps, but BJ ditches Hawkeye when Hawkeye just needs his emotional support (this is what "Would you hold me in your arms or would you let me lie there and bleed?" is about), and I think BJ tries to make up for this with big gestures, but Hawkeye is more about the day to day support and solidarity with each other.
There's also the intensity of the rebound vibe in Welcome to Korea part 1 where Hawkeye refocuses on BJ after moping about Trapper and seems to deliberately explore how compatible they can be as friends - the babysitter comment to suss out whether he'd be a partner in womanizing, his willingness to break rules and flout authority, his sense of humour. BJ passes, so Hawkeye accepts him. It feels calculated because Hawkeye needs a replacement Trapper. ("We need to get him started on his ulcer," as potential evidence of Hawkeye wanting him to be Trapper 2.0)
BJ's attitude throughout season 4, in which he stamps out his own reactions and feelings to align himself with Hawkeye. The Bus has a thread of a battle of wills between Hawkeye and BJ over whether or not to include Frank, which Hawkeye wins. In Hey Doc he also wants Hawkeye to be nicer to Frank, but in the rest of the season he's right there with Hawkeye making fun of him. In The Gun BJ stands respectfully when Margaret comes to their table and Hawkeye glares at him disapprovingly, so then BJ turns it into a joke, seemingly correcting his own behaviour.
Wheelers and Dealers characterizes BJ as resentful in a way that makes him passive aggressive, which rings very true to his character to me. In Wheelers and Dealers he bemoans being so nice and passive and lashes out. "Who cares about what they want, I'm doing what I want for a change." This obviously says that he buries parts of himself to make nice with people habitually, as part of how he interacts with people, and I think you can see him doing it with Hawkeye early on.
You also have episodes like Heroes and Stars and Stripes where BJ alternately mocks Hawkeye for getting the spotlight and lords his own spotlight over Hawkeye, because he's insecure and presumably feels overshadowed by Hawkeye.
This is all to support my take that BJ moulds himself to suit Hawkeye because they're not intrinsically all that compatible as people, and he resents being the one to do that. So later BJ lashing out with mean pranks and psychological warfare (Bottoms Up, Dear Uncle Abdul, Joker Is Wild, what feels to me like negging in No Laughing Matter, etc) and ditching/mocking Hawkeye when he's upset about something (Back Pay, Depressing News, Give Em Hell Hawkeye, Blood and Guts, etc) is a response to that resentment when he feels more secure in Hawkeye putting up with it.
I think BJ would probably mould himself to fit anyone he wants to be friends with, but I don't think if given the option, he'd choose to be friends with Hawkeye. He disapproves of several things about Hawkeye even initially - his aforementioned lack of patience with Frank, his rampant sexuality (eg he does disapprove of Hawkeye sleeping with Carlye in The More I See You, and you also have several instances of BJ making fun of Hawkeye when it comes to his attitude towards sex, eg Taking the Fifth, Inga). And I don't think Hawkeye would choose to be friends with a monogamous married suburbanite if they weren't forced together right after Hawkeye lost his last war zone bff.
My evidence for Hawkeye only putting up with BJ's late season attitude because he's trapped is that he tries to put his foot down multiple times and fails because a) the 4077 is a very small world, and b) BJ needs his emotional support in a war zone. And every time he comes back they don't address what they fought over or discuss it or reconcile it, they simply drop it because they're reliant on their friendship.
In Ain't Love Grand he sleeps in the front office but comes back to share good news with BJ and emotionally support him. In The Most Unforgettable Characters they drop the fight because it upsets Radar without addressing why they were fighting. In Picture This Margaret manipulates Hawkeye into going back to BJ by lying about BJ needing his support. In The Joker is Wild and Bottoms Up Hawkeye mildly pranks BJ back in a tag and calls them even even though he's taking a loss.
It's also worth noting that Hawkeye hates BJ's friend Leo's extremely weaponized style of pranking. He's fine with shit like exploding cigars, not fine with him getting BJ court martialed. BJ is fine with it and thinks it's funny, which strikes me as another unaddressed incompatibility that feeds into the vibe of BJ's pretty intense psychological warfare later on, which Hawkeye is generally upset by rather than seeing it as all good fun.
And in GFA they both initially intend to leave without seeing each other again, BJ trying to leave a week early despite knowing his travel orders are sus and without saying goodbye or leaving a note, and Hawkeye expecting and ecstatic to be flown home when released from the hospital only to be ordered back to the 4077 for one more week. Also in GFA Hawkeye says goodbye for good, fully expecting to never see BJ again and sad about it but accepting.
Oh also the fact that Welcome to Korea is structured as a series of horrible things happening in a war zone that bond them together through shared trauma is another piece of strong evidence for the reading that being in a warzone together and needing each others' support is why they become friends, when otherwise they might not look twice at each other.
Ultimately you can take all this stuff and also interpret it as two guys who fall in genuine love/intense friendship and put up with each other because of that, but I think there's more than enough evidence that them being trapped together in hell is a major reason they become and stay friends, and imo it's a solid reading of their relationship, and also infinitely more interesting to me.