Two of those trophies were single-match competitions (2010) which are little more than friendlies: one is played at the very beginning of the season, and the other after a brutal flight to Japan (and with no pressure whatsoever: nobody cares for that particular trophy, it's just a commercial opportunity for Asian markets).
At Liverpool, considering the money spent, he underachieved every year except the very first season (which, as I said, was really blind luck, and again it was a team he did not even build). He benefited from a situation where he basically had to compete with only three other clubs in the EPL, and still never managed to win a league; except for La Liga (which is really a minor league when compared to the EPL or the Italian Serie A), his victories always came from cups, where luck has a much larger role than his vaunted statistical and managerial skills. His football was terrible to watch. The more he asked for total control, and the more he would get it, the worst it got; a pattern he started in Valencia and also repeated at Inter. His successors were even worse but they also got much less money to spend, thanks to all the money he did not leave in the coffers.
His only real achievements were with Valencia, a project he did not start.
I wouldn't hire Rafa Benitez to manage a fourth-rated club, let alone a top-flight property, and I must not be the only one to think that if he's still unemployed after more than a year.