I think the problem is that Chelsea have had so much success with someone coming in to paper over the cracks... but they've now lost that core group of players that were part of those very great Chelsea sides - players like Terry, Fat Frank, Makelele, etc... They've still got a good group of players, but I don't think they've got the same leadership qualities as those core group of players - nor do they have the character to turn things around when things don't look great at the club.
And the board at Chelsea has done a lot to create a very toxic culture at the club. Because what they've got now are a group of mostly good players (because you don't win the league 2 years ago and keep most of the same players and just suddenly look hopeless), but they've got serious motivational problems and they clearly know that if things look bad at the club and tough for the manager... they can be the end of that manager, all they have to do is continue to not give a fuck.
I agree that they need to give Sarri more time if they're actually serious about giving him a chance to make Chelsea a club that plays fluid attacking football. I think Chelsea need to clean house at the top though - the people above the manager have been appalling at their jobs. But after over 10 years of short term planning taking centre stage and neglecting long term planning... I'm not sure that's going to happen at the club. But they need to have a board and a director of football that are working towards long term goals for the club - they're no longer the richest club in the league and they're no longer the only club that can splash serious cash - they've got no long term direction. Even their excellent youth program is just being used for short term purposes, to loan on young kids and sell them on at a profit to fund other first team signings. Look at the top players they've let go that are now at rival clubs ahead of them in the league.
That's really the first thing Chelsea need. A real long term plan to work towards. That's not saying they need to neglect short term goals - but expecting to simply buy success in this day and age requires both short term and long term planning. Especially when there's another oil club in the league that's richer, run a lot better on and off the pitch, that's got players that are part of one of the most historically significant title winning sides in the league's history (because they did just break the points total). But that means Chelsea need to operate more like an actual football club rather than a billionaires plaything - it means an adjustment of expectations at the board level... and probably for the fans too. Because Chelsea fans got a bit spoiled in the last 10 years with sustained success in the league (winning it multiple times, used to always qualify for the CL) and in Europe (2 CL finals, 1 CL victory, and a Europa League) and other domestic trophies - and in the recent past, sacking a manager and a quick change has worked out.
The next thing that happens after Chelsea do come up with an actual long term plan (if that ever happens) is selling toxic players and breaking up dressing room cliques. IMO, Chelsea have a lot of these toxic players - anyone with any sort of "leadership" role at Chelsea that didn't haul Kepa off the pitch after that refusal to be subbed off, like Azpilicueta (the supposed captain) would be on my list of players to go, regardless of how good they might be (Azpilicueta is a pretty good player, but that was unacceptable from a captain). Players that are clearly not good enough, like Alonso, Zappacosta, and Morata, also need to go. No point in keeping them around paying Chelsea wages for players that are dogshite. And then wantaway players, like Hazard, I think should probably be shipped out because when you've got a culture of players downing tools to get a quick manager sacking don't need the added distraction of their best player constantly going to the Belgian media and begging Real Madrid to sign him.
That's a bit harsh on Hazard, because despite his dickhead teammates, I think he's one of the few players at Chelsea that hasn't looked like they don't give a fuck. But a massive clearout is needed. Then the manager and DOF need to work together to sign the right types of players to meet those long term goals first and foremost - more of those promising kids at Chelsea should be given a chance in squad roles.
Granted, none of this is really realistic with a transfer ban looming over the club's head. But that transfer ban comes again from them breaking rules to sign young players... for their youth team that they hardly use to supplement their first team; which would infuriate me as a Chelsea fan, but is a mildly amusing fact if you're not a Chelsea fan... it's just an example of how the people above the manager at Chelsea either don't plan for the long term or they are all reading off different pages of the plan and aren't working together to push Chelsea forward.