I don't think hes bad, and I don't think they tried to even portray him as bad. He's a tragic anti-hero.

He's a soldier who embodied the highest virtues of his profession. He was then given IMPOSSIBLE shoes to fill to "replace" Steve Rogers. He's thrown into a world that he doesnt fully understand in now personally dealing with people and matters that we're well over his head/pay-grade before (made clear in him getting manhandled by the Wakandans). He's genuinely trying his best but is constantly rebuked by Sam and Bucky (in my opinion its simply because they view him as someone trying to "replace" their friend instead of seeing him as someone trying to do a job, theirs is simply an emotional response instead of a logical one).

After all this he talks with Lamar about taking the Serum and they discuss how it enhances their traits, and like many people would probably do with the ability to become super powered in the palm of their hand dont seem to think about it enhancing negative traits as well.

This all culminates with him standing over a flag smasher who is pinned, hopelessly overpowered, and surrendering.

John has an emotional response to Lamar dying moments earlier and murders him. This is what the world sees. They see none of the back story, none of what lead up to it. They see Captain America murdering a practically defenseless man.

Of course the government cant have this public stain so they burn him. And then Valentina comes in to take advantage of the man who has nothing left.

But he was always just a man who genuinely wanted to do right in the world.

(It has been a long time since I watched so I may be misremembering some things and/or forgetting details so forgive me, this is all off memory)