I remember the coach of the GB cycling team talking about "small gains". They looked at every aspect of what they did and how they could change it. They got 1% improvement here, 0.5% improvement there. Just doing that moved them from competing to dominating. They got the very best out of everything they did.
If a sport psychologist can improve players, then it is something which should really be seriously considered. If they could for example help a striker convert some chances which they were missing then that could make a huge difference to who wins a cup, wins a league, makes it through in Europe etc.
Football matches are often won or lost by the odd goal. The difference between a draw and a win is always one goal. How many draws converted to wins (or vice versa) can a league swing on, at 2 points a time.
If people think it makes no difference fair enough. I just get think dismissing it out of hand is the wrong way to go.