You can polish a turd, but it's still a turd.
The issue with Dyche isn't Dyche himself. It's how Everton is run. You can hire/fire as many managers as you like, sell/buy as many players as you want; the problem is how the club is run.
We've seen Everton's behaviour in so many clubs that were ultimately relegated. As the threat looms ever larger, long term thinking goes out the window. A club becomes increasingly reactionary, until ultimately avoiding relegation is their one and only priority.
At that point, there's nothing left for a Plan A or Plan B; there's no wiggle room left. It's all short termism and dealing with the immediate threats, with no chance to plan for the future. Building a whopping big stadium is not planning for the future when you're having to deal with your finances in the immediate here and now.
Too many clubs have done this and not many escape. Everton pulled a Houdini when they hired Moyes back in 2002; they were really on the ropes back then, but that was a time where they were still more focussed on sorting themselves out rather than trying to keep up with us. I'd say they're in a state at least as bad as Leeds were - maybe even more.
Dyche might save them this season, but it doesn't solve their problem. The question is whether Dyche can do a Moyes with them, but it's not 2002 anymore. They were bad on the pitch, but at least their finances weren't screwed.