I think some of you missed the point of the whole Jerome/Joker relationship. Before Jerome there was no one like him. We saw him as the Joker because the many similarities the shoe obviously and purposely inserted. After his death, go back to what his father said. He'll be a curse. You don't have to be alive or actively doing anything currently to build a legacy. The laugh isnt going to cause a killing spree, but it will inspire another broken person to take on a mantle that doesn't exist. Jerome died but his madness lives on, much like his everlasting grin. The show is pushing the Joker as a state of mind, perhaps like a desease, almost as a title that has to carry on before it reaches the actual Joker we know and then to somone. Terry McGinnis was created because the world needs a Batman, what if the world also needs a Joker? In. The future, Batman creates the Joker but the Batman also sstepped forward to stop mad men like the Joker. Yin and yang.

Jerome isn't the Joker, but perhaps was originator of the Joker as a curse. The Joker may from this point on always exist.