Eh, I can see where you're coming from. It's an interesting shower thought.
It just doesn't hold up to canon at all, nor casual examination of the major versions of the Joker.
The possible exception would be the 60s TV version. The flaw in that is that he never comes out on top in any way, he isn't showing signs of actually using his reputation as a weapon that helps him. But if you look at it from the outside, the character is most likely not "crazy", just playing the game of costumed criminals to the hilt. So it kinda fits because we all know that no villain on that show had a chance because the writers and production team wanted the heroes to win every time.
In comics, the older versions of the Joker were more criminal than crazy, but still showed definite signs of the crazy being there, and causing his downfall within the stories as they were told.
Being real, there isn't a single Joker. The various eras meant that social mores limited how he could be written. This was so pervasive that the characters are essentially not the same person other than general appearance and being criminals in some way, with Batman as their opponent.
You gotta understand, after a certain point (I think it was in the eighties, but opinions differ), each successive editor in chief (the equivalent of a show runner or whatever) ultimately decided not only the overall tone of the publisher's titles, but often managed the limits the company was allowed to go to.
If you look at something like the death of Robin (Jason Todd), or the premise of the Injustice "universe", that's what the Joker would be in any semi realistic sense. He's not a criminal genius, he's just a psychopath with violent and homicidal urges.
There's also the whole "agent of chaos" aspect that gets used sometimes, and the Heath Ledger version is a fairly believable take on that without being too comic-booky. But again, that's still an artifact of the limits placed by whoever has a final say. When it comes right down to it, the Joker being "sane" simply isn't a useful story for DC past or present.
All of that comic geek bullshit aside, I would actually love to see an elseworlds story with your idea. Hell, I wish I could write it and get away with it. They'd never hire my ass to do it, and I ain't fucking with copyright and trademark lawyers on retainer, but I could see how the story could be done.
Even with that, though, it would HAVE to end with the Joker losing. It would never be accepted by the public as a majority otherwise. If I was writing it, though, that loss would be him finally on death row because a single error convinced the right people that he wasn't criminally insane. No more Arkham, just solitary confinement and a drip from an IV.
That would be the final panel, too. His arm, white from the chemicals that changed him, with a needle inserted, and nothing but the typical hahahahaha that gets done when he's laughing, starting in large letters, then tapering off to ellipsis as he fades to black.
Yeah, it could be a fucking amazing story arc.