He has been managing Everton, on a shoestring. The fact he even keeps them consistently competitive is admirable.
Let's face it, how many PL managers have had the success you are expecting of him?
The squad depths at Everton's level mean they need to make a choice between Europa and the league. Look at the teams that did "well" in the Europa or took it rather seriously, where are they now? Boro, gone. Bolton, gone. Martin O'Neill used to deliberately play reserve sides, and rightly so.
Only Fulham managed to do a good campaign without screwing themselves up in the league, and going by your logic it was that sort of "display of ambition" you talk about that landed Hodgson the Liverpool job
Arsene Wenger has not picked a trophy for bloody ages, is he a crap manager? Fact is in Moyes' time few managers other than SAF, Mourinho and Ancelotti managed the sort of success you crow about. With significantly greater funds and phenomenal squads at their disposal the likes of Mancini have won the league and Di Matteo the CL. Does that make them better managers than Moyes? I reckon Moyes is better than the two of them, even when winning the CL with that Chelsea side is a more difficult task than winning it with Barca. But there was a lot of jam involved in that, not RDC genius.
I would always take Mourinho ahead of Moyes, no question, but wouldn't have a problem with him at all. Sure, we would need some learning to happen, which is not the end of the world when you are talking about replacing the most successful manager ever.
Guardiola? I really don't get the hype. He is fine but with such great players at his disposal, ample funds, every man and his dog wanting to go there... He managed the transition from the Ronaldinho era well, but I wouldn't put that beyond most reasonably good managers. The rest was a stroll and, if they ever needed to shake things up a bit all they need to do was go raid Arsenal and other feeder clubs of theirs.
Easy job, so easy he got bored with it. A manager that gets bored after winning everything for a couple of years... fecking hell, why would we ever want THAT to replace SAF?