I have no evidence of this, but I think the correct answer to the OPs question about why Kilmer didn't return is obviously because of Batnipples and Batcodpieces. It's the only logical conclusion.
I liked his Batman over George Clooney who I felt was playing George Clooney and not Bruce Wayne.
But Bruce Wayne's outward facade and public persona IS
George Clooney, essentially. Dashing, wealthy playboy with some prominent public causes who never settles down. I'm not sure that George Clooney isn't right now out spending his nights fighting crime as a vigilante.