I'd use the Star Wars analogy here. Can Star Wars support adult stories like Andor? Sure. Can it also support Jedi Babies*? Apparently also yes. But when you say "Star Wars," 98% of gen pop expects the 1977 -1983 films. A FN@F HHN house is going to be based off the first game, or the movie, or some combination thereof, no matter how dark the series eventually gets. I think it's disingenuous to pretend otherwise.
I'm with
@OrlandoGuy,
Frozen Empire seemed more inspired by the cartoon than the original Ghostbusters (I think Millennials tend to conflate the two) but the history of the IP gives HHN a fig leaf. Potter its own walled off thing--yeah, another fig leaf, but they also don't promote the Deatheaters with the rest of the event. FN@F, while it could make a solid house and would probably move a ton of merch, would feel like an attempt to cater to a middle school crowd. Not sure that's a Rubicon the event wants to cross.
* - Don't know the official name. Cartoon where Yoda trains kids who look like Dora the Explorer.