To the extent there is a rotten core it's obviously organizational as it predates most of the squad and appears to infect the newcomers. Players who are competent elsewhere are incompetent at Everton, and at this point it's not simply poor incomings (though it is that). I sincerely hope, at least right now, we don't give up on FL as he continues to strike me as the type well suited to rebuild Everton into something recognizable. Panic buys and managerial changes and a new stadium won't change what's broken, IMO.
My very uneducated opinion would be it begins with some very steady hands at manager and player (like FL and Tark, perhaps) who embrace quiet leadership at this stage rather than holding on to former glory, paired with mature, hungry, youthful players who care about Everton's history and see the opportunity to be a part of it being restored. Bringing in leftovers and former stars looking for a payday from a desperate club obviously hasn't worked.
I'm harsh on him, but I do think it can't be great for morale to trot out a clearly deficient player in Davies year after year. Is he generally thought of as a locker room asset who cares deeply about the club? If so that could change my perspective, although it obviously won't do anything to change his skillset.