Let's say hypothetically someone did attempt another rewrite. First of all, it'd have to be competently written, which isn't necessarily a high bar in itself when looking at it's predecessor. But most people who are interested in Jeff still (I admit) probably aren't looking at it from a polished point of view, if you get what I mean.
Secondly, I want to ask what specifically is valued in Jeff as a pasta, since his popularity has been coopted by a culture who is into anime and boys with mental illness. 50% of the notoriety comes from the photograph which has aged poorly. So we can maybe make a better one, commission Trevor Henderson, whatever. How about the story itself? How does one make you root for or at least sympathize with an angsty teenager who begins killing after getting into a scuffle with some wannabe thugs?
If we go the Joker route, you can have it show the steady decline of sanity. Show some of the horrors of whats been done to push him to that point, without having it devolve into a teenage sobfest. And then if you're ballsy enough have the horror be Jeff stalking his attackers throughout the night, and the horror is specifically them having to witness this raggedy bleeding mess calling for them in gurgled rasps until he inevitably dies. THAT can be scary, someone who needs help but is refused it based on appearance, and if you wanna get deep on this, a critique of mental health awareness.
And arguably the most important thing to walk away from this with is not idolizing Jeff as some sort of hero or person to be looked up to. From both an ethical standpoint and good writing standpoint I'd rather his figure be tragic, a morbid reminder of the limits of humans, and the lengths to which illness can warp a human. I invite anyone to try this out, I'm not invested in Jeff regardless since I'm not invested in his growth or popularity.
There are a ton of good Jeff stories out there, usually they only have the appearance aspect of Jeff (and him being a murderer) in them, the rest is completely unrelated. Which at points, comes off so distrinctly that people don't even realize that it's a "Jeff the Killer" story, unless the title includes something relating to the character.
There's also Slimebeast's JTK which takes a very realistic route for Jeff Woods (I think that's the last name) but, it isn't so much a typical JTK story. Just has a bullied kid that ends up doing something very violent - if you live in America, you should be able to figure out what that is (hint, they talk about these in the news and it relates to schools).
Do I think we need a new Jeff in all of his awful glory? nah, keep him buried in the rumble. You can dig up the corpse and abuse it a little for your own enjoyment but otherwise, keep him dead.
Honestly Jeff the killer has had enough spot light, and the jeff you ar eprobably thinking of isn't even the orginal Jeff the killer. I would rather see re writes of stories that have had less spot light. I myself have re written a story but I don't really plan on posting it here.