Non-qualifiers can be a great asset. Since I usually run a 10 man team, a starter and a backup for each position, I usually try to have one ineligible and one redshirt. That way I don't have anyone wasting on the bench for a whole season. There are two other advantages as well:
First, since they cant practice, put ALL of their minutes into SH (Study hall). Usually this will get their average over 3.0 for the next season, which they will be sophs and you wont need anymore minutes in SH. If you keep their GPA over 2.7, they will come back for a 5th season (4th of playing seasons) .
And if they are Seniors, and will be coming back, you will still get cash for recruiting for them since the sim will always act as if they are leaving. Just make sure they have that GPA over 2.7 and use that extra cash in that seasons recruiting.