I think implementing rake for tournaments would be a good addition.

Since the site already aims to mirror real poker formats, adding rake would make play-money tournaments feel more authentic and closer to real-money environments.

~15% rake would probably do the job. For example, a tournament could cost 10000 + 1500, where the player pays 11500 total, 10000 goes to the prize pool, and 1500 is taken as rake rather than being distributed to players.