Yeah, note that this seems an improvement compared to the current system, but it actually isn't, because you still have the difficulty of 3 competitive games AND you need to make sure the trainees are among those getting trained. If easier, instead of using the 144/288 minute cut, you can just select the 3 players with the most minutes.
As a tiebreaker, you'd go with age > potential > salary > ID. This is because potentially you have multiple players with the same minutes: for example in this system you may have 4 players all on 48.0 and whatever the system only 3 will get trained.
It is more complicated than the current system, but 3 competitive games would be much harder for trainers.