I don't think Benitez would be considered as an Everton boss. Even though his record will probably be streets ahead of all the other candidates.
I'm partly having a little dig because Chelsea fans are always told about what a great job Benitez has done. We're supposed to be grateful to him that we're in the EL final and will probably make the CL. We're supposed to accept him as a possible permanent CFC boss.
While Liverpool and Everton is the city rivalry and the traditional rivalry, the present rivalry between Chelsea and Liverpool is a lot more bitter and nasty. I don't think Benitez will have ever gone out of his way to antagonise Everton fans in the way he has CFC fans.
It's just an example of why CFC were so dumb to appoint Benitez in the first place.
I actually think that most Everton fans will admit that Benitez has a better record than whoever it is they will get but they'll still choose the other manager.