Theory Batman is a Child's Toy
The Joker says, "Where did he get all those wonderful toys?" And, "Get a load of my toys."
This is because all the characters are action figures.
My guess is that a boy who's family has died is given some action figures. He plays with them often. But, he can't forget the death of his parents.
The kid can not deal with the death, so the blame on one of the action figures.
Also, it is important that the villain does not stay dead. But, if the action figure is depicted as dead the figures do not stay dead. The Joker along with the other figures are only plastic.
Arkham is seen as a place to put villains/Action figure villains that will not be played with for some time. This is storage for the child's toys.
Arkham is an attic or a closet. This is why not many get reformed.
Other Action Figures
There are character that come to Gotham. This Action Figures are brought over by other children. My guess is that the kid's best friend has some Superman Action Figures.
Also, there are some villains in the comics that are never seen ever again. This could be because they are given away to other people or placed in actual storage. The boy is allowed to keep some Action Figures. This helps the parents clean up the area he where he plays.
The figures get broken then need to be replaced eventually. The child gives each of his new versions of the same Action Figure but a different and similar backstory.
In the comics, there are three versions of the Joker. This could be the child having three different Joker toys over time. The child might have forgotten the original story. Or, the back story seemed too shallow as the child grew up.
Example: The Penguin is still the Penguin. But, he reforms for some time. This way the Penguin can be used as a background character. And, does not have to be put into storage.