What would you do if you had virtually incomprehensible powers? Obviously, you would use them to hop dimensions and annoy the crap out of your favorite costumed hero.
You wouldn’t? Why the hell not? Bat-Mite has been doing it for nearly 60 years and you have to admit, it’s working out great for him.
Bat-Mite is like if that kid who wanted to be Incredi-Boy has phenomenal cosmic powers and the ability to change the shape of reality and instead of becoming Syndrome and murdering supers the world over, just used his abilities to follow Mr. Incredible around everywhere and become a minor nuisance.
Only, in this case, Mr. Incredible is Batman, and Bat-Mite knows when to walk away.
Sure, Bat-Mite might be in need of a serious tailor but he doesn’t let his lack of sewing skills get him down. He goes on adventures with Batman, annoys the crap out of Batman’s nemeses, and even got his own mini-series in which he is the star. Multiple times.
He was so successful that he even appeared as one of Batman's own delusions after Batman is shot, nearly dies, defaults to a backup personality and then runs around Gotham as a crazy purple hobo because Grant Morrison.
He is truly living the superfan dream and all without using his seriously insane powers to, you know, destroy the fabric of reality.