I just had exactly the same issue, and I've only upgraded to be able to review my game against the coach.
Missing “Play Coach” after upgrading to diamond.

On web, Play Coach should be unlimited. On the apps, it may not fe fully available yet. Are you seeing issues on the website?

When it was in beta it was listed as 3 games per month.

Are you on the website?
I just upgraded the platinum solely for the purpose of being able to play with the coach and do more game reviews. After upgrading a platinum, the play coach option disappeared. Has anyone found a solution?

@11Justus11 Can you tell me a little more specifically what happened? Did you see Play Coach on Web (currently we are rolling it out slowly, it's not fully out to all users), and then did it disappear after signing up for platinum? Or did it disappear from another platform?
The only reason I upgraded to diamond was to have unlimited play coaches daily. With the base version I could at least play coach twice a day. I paid money to have less access. Or am I missing something?