I think what you are suggesting would be great for leagues. Instead of having one main league we have a league for each and every level of play with each account only being allowed to pick one league to participate in per season. The higher the league the better the prizes. For example ... Novice league would have very minimal prizes compared to Diamond league.
However I don't think its a good idea to make those with diamond level cards play diamond level games only and one main reason to this is skill wise not all players who have diamond level cards are diamond level players / Not all players who own Silver level cards are Silver level players. A newbie can sign up to Steem-Monsters today and buy his way into having Silver/Gold or Diamond level cards. It wouldn't be fair to restrict this player to only Diamond level play because they decided they wanted to start with a max deck.