So, why did they kill off the Joker - offstage, and before the show even really starts, no less - just to replace him with a character who's exactly the same with the addition of candy-related puns? Heck, they even gave him a Harley Quinn expy as well. Not that I'm complaining as I loved how it was done, but it's really weird to me that they did that instead of just using the Joker (considering how popular Mr. J is).
Probably to show respect to Heath Ledger's Joker, it might have been seen as Too Soon after he died in real life.
...but that makes no sense. Ledger died four years ago and plenty of other Batman media has used the Joker in-between that time. This isn't even particularly based on the Nolan trilogy.
I thought it just tied in with the early competition between Batman & Superman and the latter ranting about how much Batman's villains suck (Sweet Tooth wasn't very popular at all).
I'm not sure of the source, but I had heard that Matt and Nick Lang had been having trouble writing a story about the Joker and Batman. Once they switched from the Joker to Sweet Tooth, they were able to finish the script. They may have just wanted to give homage to their almost-script. It also serves to show that Batman not only takes down little crimes in this universe, but big bads like Joker.
The Langs said in an interview that they found it really hard to make a parody of the Joker when he was already funny to begin with. This, due to the fact that there are already hundreds of different interpretations of the Joker, made the Langs decide to make their own villain to lampshade the ridiculousness of Batman's villains' themes.
Sweet Tooth is so similar to the Joker that probably one out of every two viewers is going to assume it's just him in disguise, regardless of the Really Dead Montage at the beginning.
Let's look at the play from another perspectice. Let's say Sweet Tooth IS the Joker. Well...you lose the candy running gag. You lose the humor of having Sweet Tooth be a poor man's Joker...and his plan is pretty on the spot an upgrade of Jason Todd's death. It's not FUNNY. But...if you make it a guy who's NOT the Joker...suddenly, it's HILARIOUS. It adds a bit of disconnect. He's got the hilarious 'candy' puns. And you can add a little bit of surrealism to it. (Nuclear warhead. Pop Rocks and Cola...)