They kind of do, currently. Your 40-man roster is in principle what you have to work with in a season. But league rules have minimum stays, once a player is sent to the minors, so you can't just yoyo the 25-man roster up and down at will. AAA rosters are limited in number as well, and probably their managers tear their hair out with being short-handed, what with someone being sent down in favor of a fresh arm, meaning that that guy can't pitch for a couple of days (or else the majors would have kept him), and with another guy you've been told is coming up to the majors so don't use him tonight or tomorrow either. It can be done, and is, but requires a lot more juggling than is at first apparent, IMO.