I have a feeling its more of a 'It won't matter if I try to prove my innocence, they wouldn't believe me' situation. So he's probably just given up on that path.
As for the killing of his pursuers, I imagine that this could for several possible reasons:
- He feels he might be always pursued, even after he finds the person responsible, so he kills his pursuers so there are less of them he has to deal with later.
- He's such a deadly warrior that ultimately when he fights it leads to death; he's not able to hold back enough or it's just instinctual to land the killing blow in a fight where his life is on the line. (Cause lets face it when this happens in shows, pursuers of the protagonists probably wouldn't actually survive a single hit from most main characters).
- Some of his pursuers could actually be in on the whole thing, like those soldiers could have just been corrupt.
- In that particular instance he might have also not wanted to risk the girl being considered an accomplice and killed, so possibly protecting her.
Overall, I can see how his actions might not fit a lone wanderer, falsely accused of murder. But at the same time I feel that these deaths more realistically fit what would actually happen when a warrior such as Yasuo is being hunted down, with his life on the line, over a murder he was framed for.
