One argument is that by getting in a new manager, regardless of who, Everton's chances of being relegated increases by a lot.
Even those who are brave and are getting in good managers that is a good fit, often see the club going through a tough spell without getting results. Look at Bournemouth. Iraola was a coup. People that follow football were surprised Bournemouth could attract him. He got money to spend. He got a full preseason. He came into a well run club with a brilliant director of football. He started with 0 wins in 9.
Look at Lopetegui at West Ham. Previous Spain and Real Madrid manager. Knew the league through his successful spell at Wolves. The type of manager Everton currently wold struggle to attract. West Ham spent silly money last summer. People saying they won the transfer window. Results have been awful. Their football is no better than it was under Moyes.
To think that an Everton team, with one of the worst squads in the league, should be OK and play god football by replacing Dyche is beyond stupid. This Everton squad is a lot worse than the one we had when Dyche was hired. Dyche should be blamed for that, but that is not a good reason to replace him now. It would make much more sense to replace him 18 months ago or last summer than now.
People have unrealistic expectations to this team. Back to back summers the fans have pushed away and applauded sales of the teams best midfielder. None of our current midfielders would make Forest's matchday squad. They were happy to see our best one (Mangala) go 10 months ago.
Ancelotti and Lampard knew that you'd never want Doucoure on the ball in your own half. That he was a liability. While Everton fans in forums and social media kept talking about playing him as a 6 or an 8, not as a 10. When Dyche is forced, due to lack of options, to play Doucoure deeper and Doucoure does what he has done his entire career, the same fans blame Dyche for Doucoure's mistakes.
Funny, isn't it. That those who were happy to see the back of Iwobi and Onana, were the same people that wanted Everton to sign Kalvin Phillips last summer. People with big mouths and strong opinions that might be proper fans, but that don't watch football, don't like football and don't understand football.