Two obvious problems with this imo. One, it makes Jerome more important then the Joker. It makes the Joker a lesser Jerome that was his idea. Not the Joker, the force of nature. Second, they gave the Joker an origin, one that again makes him lesser.
I'm sorry, I never replied to this (A bad habit I need to kick), but I was waiting for more information on Jeremiah before I could actually argue this or not.
showrunner Danny Cannon recently said (when asked if Jeremiah would be called "Joker"):
"Well, I think that just spawned the conversation of the idea of it, of the Joker not being a one person, but like I said, it's a personality. It's a way of thinking. It's more powerful than just one person. I don't think that's just one person. I think that is a way of life, it's an ideology." That hints more at there being a 'Multiple Jokers' scenario than anything else.
As a bonus - Jerome's final words were "
I'm not a man, I'm an idea", and Jeremiah seems to act specifically like the calm and calculating Golden Age version of the Joker, while Jerome was a red herring, based on the elements of all the Joker who came before him like Mark Hamill, Heath Ledger, Jack Nicholson, etc and what everyone expected the Joker to be and act like, while Jeremiah is what the Joker actually is, and is someone completely unexpected.
This shows it, Jerome was never more important or Joker isn't going to be a lesser figure. His arrogance and ego would never allow for it. He isn't second fiddle to anyone, and the only way to show that is by outdoing it. The name ultimately doesn't matter, it's the idea and actions that make the Joker a threat. Jeremiah is still a force of nature and a threat and while he is implementing Jerome's ideas, he is doing it through his "Sane" methods thus proving he is the better Joker. He spits on the idea that Jerome wins through him,as he died while Jeremiah (or the Joker) lives. Jerome created a cult in his death/resurrection/death, but Jeremiah easily got them to rally around him in one episode by proving his effectiveness. As for the Joker origins making Jerome and/or Jeremiah, a lesser Joker: Killing Joke (even with the multiple choice origin was an origin that a lot of writers used or claimed as the main Joker origin for decades), Lovers and Madmen, 1989 Batman movie, among other gave Joker in one way or another and that still made him as much of a threat and dangerous figure regardless. While the mystery is what makes Joker such a terrifying figure and well loved, it isn't the only thing. This could be considered another multiple choice origins of sorts. The comics doesn't define how this Joker would be look at, as well as vice-versa.
In fact, someone recently brought up this interesting fact: "This one is a little more nuanced. Honestly this is kind of brilliant because it leaves a huge mystery still for the Joker's origin because the answer is......we don't really know. Clearly he had an extreme reaction to the gas I mean we saw him flipping the hell out and knocking stuff over trying to fight it (Maybe it was just painful?), BUT there are some things that point to Jeremiah possibly already being crazy. First off, when Jim and Bullock pointed guns at him in their first meeting he seemed waaay too calm about it. Secondly, he did make up lies about Jerome which resulted in him being abused. Thirdly, Jerome clearly believed that he was putting on an act and that Jeremiah was really just as crazy as him, he said as much. On the other hand it could be that the experience left Jeremiah delusional about what happened I.E. (Sometimes I remember it one way, sometimes another). We saw all of the same effects as the first Joker gas so why would that one effect not work? Jeremiah said that Jerome's gas was a "dud", but it wasn't Jerome's gas...it was Scarecrow's and I'm sorry but he seems to know what he is doing. Why would his gas fail? Have we ever seen scarecrow's gas fail anywhere else? No, they work exactly as intended. If it is the case that Jeremiah was made crazy by the gas then it makes the Joker story more poetic. Jeremiah created Jerome by creating the circumstances that would get him abused, and Jerome created the Joker as a result of his madness. Joker created Joker."