Suggestion - In my opinion at the end of the season, a player's injury should disappear. An off-season should mimic just that - a real off-season.

A player's injury should be healed and players should start with high condition and motivation.
It could even be that some players get injured during the off-season and appear at the start of the next with an injury - that's just like real life.

Just my 2 cents worth.