Few suggestions on improvements.

Sports psychologist. Decreases energy loss and prevents tilt.
Mentality - a new attribute. If things go bad, a player with low mentality will be likely to tilt - play much worse throughout the rest of the game unless certain conditions are met (to de-tilt him) such as taking baron. A sports psychologist will prevent this from happening as much.

Injuries and random events which stop players competing for a temporary amount of time.
Player to coach. Players who retire/get old may turn into coaches, which allows a team to convert an older player into a coach for a set amount of money,
Those are actually good. Bumped.
"Sports psychologist" No problems with this one.
"Mentality" I would like this, I replied to one other suggestion with the idea to implement some kind of person traits system. This could work as one personality trait. (https://www.mobamanager.gg/community/forum/topic/show/3384)
"Injuries and random events" If you implement injuries you should have some kind of medic with 2 stats, decreasing the risk of an injury and helping with the recovery of an injury. And maybe for an extra fee, you can send your player to some kind of specialist to make your player recover from an injury faster.
"Player to coach" I don't think this will work. Cool idea (from FM) but more suitable to Football Manager type of games, and atm this game isn't on that level. Maybe on the future.
Why not player to coach? Many league players become coaches after they retire, and it'd be really easy to code. Probably would take less than 20 min.
For starters, the staff can't even be renewed you will most probably lose the player if you don't want to pay extra for him. The staff doesn't have much of a "personality" or whatever. You can get attached to your players but staff will just rotate every 25 or whatever days.
So? You don't lose anything for doing it, not to mention that it's not just about you getting attached to players, but having players' history written down, and other well known players (such as the ones from the top teams) being recognised by people, it'd be a cool touch.