Hey, "crazy" or not, sometimes it might lead to something, even if not what originally thought.
For example, there could be a new staff such as an "assistant coach" (please, not with the current system wages though, they're turning out to be as expensive or more than players).
Assistant Coaches could "specialize" in either offense, defense (with prefered systems or if you'd like, a bonus one and a penalized one), coaching a specific position (and giving a small bonus to it either in training or game) or something like that (feel free to suggest crazy ones
).
Contract shouldn't be a skill of a coach, IMO. The system, if there's a better one, could maybe be adjusted (hopefully).
I'd say coaches could get better with experience, not training (right now, there's no one to train them in-game?). So, I guess there could be "layers" of "skill", much like players? The better the skill, the better the effectiveness?
As for further "other" possible skills for coaches... hmmm... maybe "tactics", which would mean that the team would adjust quicker to the other teams systems. Also "Motivation", a small boost to players efforts for a few minutes? "Management" as an improvement in managing players minutes better according to exhaustion, needed minutes for training and game shape (a guy can dream right?
)
There, 3 more crazy skills and a whole different crazy suggestion. We might as well throw it out there, maybe something cool can come from it