At certain levels of upgrade the resting time of players decreases eg every 4 levels of upgrading it also helps to decrease resting time before you can train again down by 5% or something like that. So each upgrade still increases the players recovery time but then the more you upgrade the infirmary the closer you get to not have to wait as long to be able to train your team again. But just make it cost a heck of a lot to upgrade it to that. Maybe even have a different costing price and make it a choice eg DO you want to upgrade just to increase the players recharge time or for a more costly upgrade also decrease the time they have to rest after each training or game. but still maintain the every 4 levels before they can even contemplate it.
Infirmary
The training center already has a similar effect but instead of decreasing the reactivation time it increases the efficiency of the training the infirmary (hospital ) shouldnt take effect on how the team trains