I think, with hindsight, the main problem the post-TWS movies had with Bucky is the torture.
The broad consensus in modern western media seems to be that Torture Is Basically Fine. It works. Torture is an effective way of extracting accurate information. And because that alone isn't enough to make it seem legitimate, there's another failsafe: Torture works only on bad people. Villains crack under torture, and heroes don't.
This is how media creates a culture that finds torture justifiable. Especially media that is largely sponsored by the US military, of course, who in a post-Abu Ghraib, post-Guantanamo, post-CIA papers world has an interest in creating public indifference (or straight up support) for torture, but there's torture in animated movies for children, too. It's ubiquitous.
In real life, torture is horrific violence inflicted on our fellow human beings, that traumatizes both the victim and the torturer, creates heaps of false information, and has no discernible benefits. It doesn't work.
But in fiction, it must work, every time, because if it doesn't, then that collapses the entire structure, doesn't it?
He's a character who is tortured into complete submission. Who is given electric shocks to the brain to erase his memory, but he still holds onto his own humanity. He is tortured into doing horrible things - the torture works - but it doesn't work completely. He breaks through it. He's beaten, abused, violated on screen, but - and this is important! - because he overcomes in the end, he's not the villain. His story evokes pity and sympathy, not suspicion.
With hindsight, it is clear to me that the mind wipe scene was meant to inspire disgust in the audience. Bucky's terror without fighting back, his defeated acceptance of the inevitable, the slow, lingering pan up his unclothed body. This is emasculating; at the time a lot of meta has been written about how Bucky is shot like a woman in a rape scene.
He submits. This is meant to be suspicious.
But it completely backfires, because what is shown and what follows is the story of a victim of unspeakable abuse finally breaking free from his abuser in a show of awe-inspiring mental strength.
(and also through the power of gay love but let's not get into that)
That's a problem. By complete accident, the film ends up saying Hey, torture is maybe sometimes bad? And that cannot be allowed. There is a more conventional torture scene in the film, where Steve and Sam throw a guy off a roof to get information out of him, but that almost doesn't matter. This is the one instance that makes the whole house of cards come crumbling down. If Bucky is a victim, then torture is both bad and does not work.
It is obvious to me that what followed TWS didn't know how to reconcile that. CA:CW felt extremely jarring because it treats Bucky with so much suspicion; it even retcons in the trigger word nonsense to justify that suspicion. Bucky has to earn trust. He has to redeem himself. From what? Not being able to withstand seven decades of torture?
Well, yes, the film says. Torture only works on bad guys. Bucky allowed the torture to work on him, and so, has proven himself to be untrustworthy. The abuse he suffered sullied him. He has to earn back his moral righteousness.
I want to stress that I do not think any of this is intentional. I don't think there was a meeting in the writer's room where they talked about how they accidentally made it seem like Torture Is Bad Maybe, and how they could reconcile that. If that had been the case, CW would have been a more honest movie. But looking back, it is clear in how the directors talked about the characters after CW came out, and in the baffling writing choices they made, that they were trying to breach this disconnect, without being aware that this is what they were doing.
For the fan spaces I hung around in at the time, where cis men were a minority, this was baffling. There's a reason post-TWS fic almost exclusively talked about Bucky's recovery, not his redemption. There simply was, in fandom's eyes, nothing to redeem him from. CW made clear that w completely misinterpreted TWS.
I'd love to go back in time to observe what the fallout from TWS and CW was in male-dominated fan spaces; how they talked about Bucky in 2015 and 2017.
Anyhow. With the benefit of hindsight, it is obvious to me that no one involved in the writing of CW and what came after took a moment to actually think about the themes and motives of the movies beyond the shallowest surface, and not just with regards to Bucky.
TWS ended up taking the tamest, most inconsistent anti-torture stance possible by complete accident and that could not be allowed. It had to be forcefully retconned. And that's why, in my opinion, post-TWS Bucky ended up being Like That.