The reality is that whatever your opinions are about the man, Joe Biden just isn’t really inherently funny. Sure you could make fun of him for being old and saying dumb things and generally being inept, but they already did a whole episode about old people. They could rip on the ineptitude of the government as a whole, but I don’t know how they’d connect that to the people of South Park. Garrison as the proxy for Trump worked because the character has existing relationships with the people in the town and that provides humorous stories.