The first one was just like a bad musical without the music. It was melodramatic, inconsequential, vacuous, had stagey set pieces, bold themes slapped in your face, garish set design. Joker 2 can stick in a pop star, some songs and the tone doesn't even need to change from the first.
A character grandly singing about where can they get some antipsychotic meds, wouldn't be any less subtle than the hospital scenes in Joker.
Obviously it would create a dissonance within a section of the fan base who wouldn't allow themselves to see the similarities.