I think the best training idea is that the players don't need to be played to receive thei training.Usually is every sport the training is receive before the games not just during the games.Also...
1) This is the case in almost every management simulation game out there. Players get training points regardless of whether they play in actual games or not. The reasoning behind why the creators of Buzzerbeater's chose to create a training system that doesn't do that has never been adequately explained. Making this simple change will fix a huge number of problems with inflation within a few seasons. It will also allow new teams to be competitive sooner, if the focus on training.
2) Also, most simulation games have some sort of set prices for coaches. Buzzerbeater already has this via the hiring internal system. Why not simply eliminate the Staff Market System and let each team hire whatever level doctor, trainer or pr-manager based on that predetermined price range (like the trainer salary ranges below). Names could be auto-generated the same way draftee names are generated.
Basic - $5000
Competent - $10000
Advanced - $15000
Superior - $25000
Exceptional - $35000
World-renowed - $45000