It would also massively reduce the number of players. Competitive multiplayer games rely on large active playerbases for fast and fair matchmaking. That's why free to play has become the dominant model for these games. If you have to pay $1000 to play one of these games, they have no chance vs. the competition.
Obviously you can't completely solve this problem, but you can minimize it as much as possible.
Also these sorts of "trusted clubs" do exist for certain games (e.g. FaceIt for CounterStrike) but ultimately it still just relies on anti-cheat to establish that trust.