Do leopard geckos HAVE to eat live food?

No. People feed leopard geckos "pinkies" for various reasons. To boost nutrition during a geckos pregnancy. To give a gecko a large feeding so as to not have to feed it for a week (this works well if you want to take a vacation). Some people just think it's entertaining. A Leopard Gecko does not "need" to eat baby mice. Crickets will do.