Interesting. I would not agree this is the case. On the surface, this does appear to be Bucky's 'arc'. However, Bucky's flaw or his need never hold him back throughout the series physically or emotionally. He's not forced to reconsider his actions because of mistakes or consequences, but because Sam outright tells him to grow up in ep5. His 'journey' skips out any meaningful struggle and goes straight from the beginning (PTSD) to the end which is a little less lost and a little more redeemed. In that way it's kind of like reading only chapters 1 and 30 of a book, with colourful action pictures in the middle to replace the actual content.

In theory, I totally agree with what you're saying and redemption SHOULD absolutely be his arc. But because none of his actions force him to reconcile his inner demons and because his motivation for helping Sam (throwing himself into a world of chaos again) isn't shown and doesn't haunt him, then his final redemption is left a lot weaker.

His nightmares don't count as haunting him though because they don't hold him back in any way after episode 1.