Ratings in rapid > ratings in blitz > ratings in bullet

I noticed that it is rare for sub 2000 players to have a rating in bullet higher than the rating in blitz or chess. It is usually either similar or the rating for faster games is usually lower or much lower than the rating in slower games.
Why is that?

Player pool strength: bullet > blitz > rapid > classical
Top players play bullet & blitz because of engine cheating and thus lower the rating in the pool
Veginners play classical and rapid because fast time controls are too fast for them and thus raise the rtating of the pool

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