I think that something interesting could be made of it, indeed. ^_^
Is trying to prove you can be better really that wrong?
well, one can always go too far, even when doing a seemingly good thing.
I think the idea is that the actions are there but the motive of "being a better person" shouldn't be to prove that you are a good person, it's to help other people.
It's a very interesting idea, at least from my point of view. If I can be so bold, it's very much an example of the Then Let Me Be Evil trope, so you may be interested in exploring that. Either way, the villain vehemently returning to evil due to realizing how little they are trusted is a very realistic idea; people break under the hurt and strain of realizing that they are being prejudged all the time.
You've got it backwards; the Heel–Face Turn is when a villain turns good.
Yeah. It's not that he's turning back to evil due to the hero. It's that he's refusing to be evil again in a misguided attempt to spite the hero.
"Villain turns good just to spite the hero." I love it. This has enough legs for a full-on story. Please write it.
In the same vein I can see a Face–Heel Turn version, except my idea is that the hero turns evil to prove to their villain that being evil is easy (which would be pretty funny in a more comedic work with a less competent villain).
So, I had an idea a while back. It was technically an idea for a Batman story, but I think it works well in a lot of other cases.
Supervillain, or criminal gets out of jail. No one really believes they're reformed, and said criminal is even secretly considering trying something again, but then the hero of the story confronts them and give a we both know you'll try something, and when you do, I'll be ready speech as a warning.
....and the bad guy gets pissed. He's pissed the hero is so sure he'll commit a new crime. Sure, he was thinking about it, but it still irks him that this ass is so sure of it.
He's so pissed, he decides that full Heel–Face Turn, entirely out of spite. He doesn't care if he can't get a job, if crime is literally his only option. He doesn't care if he starves and dies. He's going to never commit a willing crime again, all just to spite the hero.
And he sticks to it entirely. He's doing it for all the wrong reasons, but he's reformed. The Power of Hate wins the day.
So, interesting idea....or stupid one?