"I don't like bullies." -- A superhero that the movie got right
Superman doesn't like bullies either, hence his decision to teach this one a lesson.
I don't buy your premise that Superman himself is a bully here. Is he being a bully when he arrests a bank robber? There's a huge power differential there, too. Or what if he punches a Nazi? Clark was clearly not the only victim of Rocky's abuse, and if he taught him a needed lesson, maybe the employees and customers of that diner won't be on the receiving end of Rocky's bullying in the future.
Mind you, as I keep saying, I do think tone matters. Personally, I'm not altogether comfortable with the way Superman terrorizes Manchester Black and company in the much-lauded "What's So Funny About Truth, Justice, & the American Way?" That's played dead serious, and Superman is threatening real harm. But the
Superman II scene is intended as a cathartic laugh, and it works for me on that level. I'm not disposed to overthink it.
I liked the way Cavill’s Clark got a thematically similar scene (obviously intended as a nod to the original) while offering a different, equally satisfying result.
Yeah, I didn't have an issue with that one, either. Superman, on a basic level, is a power fantasy (as well as other, nobler things). You'd have to be a better person than I not to enjoy seeing him meting out a little justice to the bullies and abusers of the world.