No, you are doing nothing wrong.
The interface assumes that anybody that has some subscription will always want to play with as many cards as possible. From comments here and elsewhere it is clear that this is not the case for at least a sizable amount of players.
They may know a few physical sets and want to try out new cards, or they learned playing here without subscription and want to try more sets vs. bots, but (like you) get overrun when facing 8+ new cards in a game.
I'll put this into the internal discussion of how to best allow this.