I can't speak to China, but having spent most of the past decade in India and Sri Lanka I can say the problem there is that nobody is willing to unilaterally disarm. Everybody agrees that bakshish is deadweight loss and inefficient, but if Person A stops doing it and Person B doesn't, Person B gets more of whatever the finite resource in question is (slots in a school, permits, gasoline, whatever).
Xi Jinping has disciplined millions of officials as part of his anti-corruption campaign. That cannot be some corrupt way to silence dissidents while being popular with an allegedly corruption-omniscient citizenry.