Boosting one player confidence by selling his jerseys to the crowd is a good one.
Doctor have to have his influence already, measured by his level. If lvl7 cannot cut in half (or less) 4 week injury, Im not sure if he has any utilization in this game.
But he could have an effect into enthusiasm which would not drop so fast or something (while could not raise more than it is limited now). Seems to me acceptable that good health have influence on this.
And there could be a coach which allows you to train player more beyond potential soft cap. So if training slows down because of it, this trainer can keep it coming for another several levels. This one would be good, because Im not sure what managers do if someone stop to train right before training of some needed levels, so have to sale a strange hybrid.