I guess the progression could be like X amount of wins in unrated to unlock rated. So unrated is like Leveling and rated is Endgame. Would force unrated to be a necessary gate.
Add a weekly repeatable quest at Wolves' Den Pier which asks you play one of each: Feast, Borderland, Seal Rock, Glory, Astragalos, for some reward like 1 wolf collar + option of Cracked Crystal, Cracked Clusters etc, those sort of items that people can make money on.