Do battle stars matter after the first play?

I know that you need to hit 3* in a battle to use sim tickets for it, and there are achievements based on 3*'ing all battles.

But once you 3* a battle for the first time, does it matter when you replay? Like are your chances of getting better drops (like that char shard you want) influenced by how well you win the battle? Hasn't seemed like it to me, but isn't it odd that you don't get more rewards for better play?