Whoops, there I go thinking about eduction first and baseball second. I must be having one of my silly days, carry on :-)
The reality is, a very large percentage of players and their families value the baseball more in the short term than the school or academics. While you may be able to fend that off - don't fool yourself too much unless you've faced those choices yourself. Things can become different when they become reality.
I saw players leave Stanford for far lesser schools both academically and athletically so they could play. No, in those cases I don't think they were forced out, but the reality of being #3 (or even #2) on the depth chart at their position was too much and they gave up one of the best educations available for the chance to play (more) baseball.
I have also seen many a parent come to this site, ready to find any school they can so that their sons can continue their baseball playing career. Even in the face of a complete mismatch academically. I'm not judging them, just stating what I see as the reality
Our sons never faced this decision, but if they had I wanna think we (parents) would have insisted they stay where they were...for the education. They were both at great schools. But I cannot guarantee it wouldn't have been one heck of a debate on the subject. And coaches know this dirty little secret I am stating...and will use it to get players out.
Yes, it does happen.
Bottom line, when push comes to shove on playing time, the player (and often the parents) seem to pick playing baseball over picking/sticking with the best school.