WM: Your comparison does not stand for the following reason:
In Minor League baseball, only the cream get in. Those who have shown no aptitude for baseball do not get up and decide “I’ll start now”, and get a contract. Furthermore, if you don’t make it to the minors (e.g., you are mediocre in college), you have to get a job doing something else, thereby reducing the number of required spots.
Both of these are not true in learning. If someone decides in Bais Medrish of Kollel that they want to learn, they are given the option to do so. Furthermore, those who have no chance of “becoming the next Rav Pam” are not told to get a job, but are allowed to remain in kollel, expanding the number of positions needed.