Maybe for the daily games, the answer could be a dynamic division assignment similar to what duels do - there is some preference for sending players to higher or lower divisions based on their progress, but you could technically wind up anywhere. It would just be very rare for a top player to be in the lowest or a new player in the highest ones.
That would create some steeper competition as you go and still give newer players a chance to win, but without the massive wall that is Champs.
And I agree - WAI Champs is a bad thing, you should be able to play Easy for Everything.
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Guardian of the Tower