Disclaimer: never have a personal coach before. Did play for a while in a chess club where the team leader is about 2200 FIDE.
Sorry, I'm rather confused. How are these prices exorbitant for professional coaching? I can't imagine you can get a tennis coach for your kid for less than $50 per hour.
The results of every rated game (played at tournaments etc) are reported to a rating body. Back when I played (low level) competitively, rating lists were published every couple of months in paper form; nowadays it's all online, of course.
Sounds like another instance of centralization that must be disrupted by the blockchain
The system has been tweaked over the years as there small statistical oddities.
But official ranks are determined after playing 10-25 games in “official” tournaments.