This discussion is pretty interesting, however from what I see, only big teams are listed but not the small teams. I would say that for a football team to succeed, there must be the presence of a coach and the 11 players on the pitch.
For this, I will take the comparison of Carlo Ancoletti and Otto Rehhadel, the former having a team with big players yet producing minimal result and the latter leading a team of unknowns winning the Euro 2004. Maybe using Rehhadel may not be a fair comparision, I would use Mourinho instead. This can also be applied to Inter's case. Many top stars yet no1 to orgainse to them. They play like 11 individuals compared to 1 team.
A coach's job is to organise the team and get everybody involved. As Sebastian said, a coach does more things compared to what is seen on the pitch. He observes trainings and decides who to play, when a player misbehaves, the coach also need to think of how to control him so as to compromise him and not let him affect team morale. This can be highlighted in Roma season 2004 to present. Tactics are also involved, such as man-marking and making use of player's abilites to the maximum and bring out the perfect formation.
Sometimes a coach tactic does not work, yet the team wins, due to the presence of top players. But sometimes a coach tactic works brilliantly, however no result is produced. Why? Because it is due to luck or the players at his disposal cannot produce the goods. This phenomenon is pretty common for mid-table teams, as they know how to break big teams down, yet they don't have the players to do so.
For example, Wigan. Paul Jewell may know how to break big teams down, yet the players cannot do it due to the abilities. Somehow I feel that Benitez also has this problem as Crouch cannot finish, so the starting 11 also matters. For big teams with a strong starting 11, they can just win teams with minimum effort. Just look at Barcelona for example. Rikkard just has a worldclass midfield and attack at his disposal and they can win titles. Which is y I believe that for big teams, u don't need a world class coach to win, but a decent coach will do.