Yes, you are correct, PGA Professionals usually go on to become assistant pros at clubs. All players have to meet other criteria to play on the tour. As a PGA Assistant Professional at a nice mid grade club, you eat a lot of shit and work long hours for little to no money. I would know.I believe the PAT in golf is part of becoming a pga pro, not a tour player. For that you go through q school, korn ferry, then the pga tour.
Unfortunately, becoming a pga pro doesn't mean you'll actually play much golf.
Let's focus on how we might be able to adopt the PGA model and make it work for pool.