I also could see if players like a particular coach

and that coach leaves for another school, the players could follow that coach to the other school (at least to an extent).

I agree with your first statement too.

All that stated, it is hard for a recruit to know how he is going to like a school from just one recruiting visit. I would venture a guess that recruiting visits at most schools give the player practically no idea what the school is like on a typical, non-football weekend, and whether that fits with what they're looking for... That's why I think the rule, while it has it's warts, is a net positive for the student-athlete.