If Batman and Joker are peers, how is a mature Joker around to meet Bruce Wayne’s parents, who were killed when Bruce was very young? There must be a 20 year gap.
My take is that Arthur Fleck isn’t supposed to be “The Joker” that is Batman’s nemesis, but just some prototype that later on inspires that guy. Fleck probably stays locked up in Arkham forever, but 15-20 years down the road some kid who remembers seeing what he did on that talk show will take up the identity.