Gloves matter, depending on where you are. Pitchers want big gloves to help hide the ball. Outfielders would too for that one that just got away. Infield is a time thing. You have little. Smaller glove is better. I'm sure today they can get custom made gloves, just like bats.
I don't know if the difference between bigger/smaller 3rd base glove and a SS would matter, but if that's what they want to do, and can, why not? A pitchers glove and a SS/3B guy was like a boat anchor and something you could catch a ball with. :-). Of course that was when Denny McClain was winning 31 games.