I wouldn't say the Joker "won the people over" so much as he dropped [fake] dollar bills from the sky.
Returns establishes that Max and his family have outsized power in Gotham, the new mayor is weak for a multitude of reasons, and that the city is fucked up enough that people will back the heroic recently discovered to be true urban legend if you plan his appearances well enough. (Also, why they frame Batman...)
Burton understood the perverse mental illness of the Batman mythos. Who watches a super hero movie to have fun and see action when you could be brooding at the sadness?
Also, Batman Returns has the greatest scene in maybe any movie ever. When they show Bruce Wayne just sitting in the dark waiting for the Bat Signal to light up.
