In the real world, we had someone inspired by Dexter (not the cartoon lab character) to kill his own brother. Another guy was inspired but was discovered and stopped after his first killing.
A few decades ago, there was the Tylenol copycats.
There was the Zodiac Killer and his copycat.
We had the Jack the Ripper-inspired murders in London a few years ago.
This is in our world - the DCU takes things to the nth degree...
It wouldn't stop them (any wannabe 'successors') from trying, though.Plus, DC has made the Joker so montrous that it seems hard to believe any "successor" could possibly be as bad as him.
Just to clarify, however, this is with regards to those who, inspired by Batman killing the Joker, want to die via 'suicide by Batman', rather than just those 'merely' inspired to be like, or pay homage to, the Joker.