If you like the players you recruit, stay at the school. Build it into a winner. That's the premise behind the game.
The whole concept of players taking recruits with them when they shift jobs creates a host of headaches. For example, what happens when a guy at a low-prestige D2 or D1 program moves down and takes a position at a high-prestige school a division lower? Quite likely the guys a D+ prestige signs in one division would have been on the screen for an A+ at the next division down, so...? What about at D1 when someone from a doormat Big Six program moves to take over a mid-major (given current hiring logic, I don't know if this is even possible...but that's a rant for another day...). Are we going to see Vanderbilt's recruits suddenly depart for Tulsa or something? Think of the potential for abuse as players grab low-success programs in high-human conferences for a year to use the league's bonus cash to recruit, then transfer to a less-competitive league, taking their recruits with them, Think of how badly it would suck for the other humans in the conference to see a school in their membership suddenly disintegrate because the coach got restless feet and took the young nucleus of that program with him.
I hate to bring the real world into a fantasy game, but in this case I think the parallel should remain. Kids sign their letter of intent with the school, not the coach. Their obligation is to the school, not the guy who persuades them to sign four years of their life away. Allowing the players to go with the coach would be horrendous for the game.