Did he do well at Napoli? They dropped from 2nd to 5th under his stewardship. Sarri who was much maligned at Chelsea followed him and performed better, amassing far more points consistently over 3 seasons - 2nd, 3rd, 2nd. I think his points totals were in the 80's and 90's. Whereas Rafa's were in the 60's and 70's.
For perspective he followed Mazzari who finished 6th, 3rd, 5th, 2nd, and won a coppa italia. He also left Rafa with the gem that was Edison Cavani that allowed Benitez to sell and spend 105m on the squad with the aim of usurping Juventus. He failed but finished 3rd and won a coppa italia for them again. So they stuck with him. He then finished 5th which was seriously damaging after the previous seasons investment and the fans weren't sad to see him go. Missing out on the CL was massive, the fans were hugely disappointed.
Chelsea? He was only there 6-7 months. He did a good job with the fantastic squad they had.
Liverpool - He did but in his final season they dropped from 2nd the previous season to 7th. It was defo time to go.
At most clubs, bar us, the fans are ready to see the back of him after 2-3 years. There has to be a reason for that. So people can claim he played attacking football, point to stats, but the fans are the ones watching the actual football and he hasn't proved a popular watch over the years. Everton fans are already grumbling. At Real Madrid he showed his attacking deficiencies as a manager and someone who could not deal with big players. Tried to find a way to play attacking football after the fans got on his back because he was boring everyone to death again, (handkerchiefs were out in pre season), and ended up losing all defensive stability. Consistently upset the players and generally did a **** job. Zidane went in, sorted it out in no time because of the talent they had, finished 2nd and won the CL. Following season delivered the title.
Lets remember too, when did Rafa last do anything of note as a manager? Napoli Coppa Italia? That was yonks ago. When was the last time he played a style of football in keeping with the times? Never. He has his own style, and its defensive counter regardless of the players he has.