Moore and Miller only wrote a handful of stories though. Man of Steel isn't as good as Year One, but Byrne only used that as a prologue and by the end of his run was writing all three titles while drawing two. At this point while Miller's Batman catalog still isn't huge, he's written arguably more bad Batman comics than good. They brought in Perez a little later to basically take over as the new Byrne and I'm pretty sorry it didn't work out, because I do think he's a better writer if a little less quirky.
The "best Superman writers" thing is tricky. Strong modern storytellers and best folks of the late 80s... generally I don't think their Superman is really above their best work. They're not the "best Superman writers" because of Superman, they're the "best" because of who they are as creators. It ends up being a pretty bare comparison.
And there is a pretty big misconception about STAS. It was largely based on Byrne, but the assumption that the power levels were the same and is incorrect. Those power levels are really the golden age levels just with consistent flight. Byrne's second issue of Action has him lift a mass that he describes as, "only a couple of thousands of tons." That comment wouldn't go anywhere near the cartoon.