The coach doesn't do much. On court the player is on his own and are not even allowed to get coaching from the coach. Dull pays uncle Mafiosi 50% because he coaches him on court illegally. That is wrong.
The player is alone and has to do everything themselves. Even off court they have to do all the physical work. At pro level technique is formed and it doesn't change. A coach is more like a companion and advisor. A coach is not even crucial. Federer has played without a coach for instance. Even caddies are allowed to give advice in golf during play and they get 10%. Why should it be different in tennis when coaches can't even talk to players during the match?
The coach does so much. You can't go it alone. They devise strategies, get them mentally strong, are a sounding board, etc etc. People thrive when they have support. It's vital to improve and know what to do to get better.
This is pretty good, but what about travel expenses? Does the player cover that as well? I imagine travel is a huge expense. Perhaps the real big shot players have their own plane or whatever and the coach can ride along.
From what I've read, the player pays for the coach travel and hotel.