All you need to do is mark the pivot player and bam, team falls apart. Instead, you need a playmaker who can play up by the striker or behind two all-around CMs or out wide. Ozil can do that, Isco can do that, Oscar can do that, etc.
Of the teams you mentioned, only Barca plays with a real pivot, and not really to great effect anymore. Guess you could make a case for Lahm and Bayern but what they do is not in any way the classic pivote.
At Real, for instance, Xabi Alonso and Modric are box to box with one being less adventurous in the final third, just like Khedira could be for us, with Isco playing ahead of them or dropping behind one of them if necessary (or pushing out to the wing, etc.).
A player who screens the back four also needs to be the outlet through which the team can play when the ball is with the CBs, if that player "sits" like so many want, like the classic pivote, then he's easily marked out of the game and the team is forced to play through their fullbacks. This is not good. Just look at Spain and Italy recently. France played both games with 2 all-around B2B midfielders and Cabaye as a playmaker. Time after time, Cabaye was up the pitch ahead of his CMs, and the CMs actually took it in turns pushing out wide (even overlapping with the fullbacks!) so the wingers could cut inside. Nobody just "sat" or played any kind of traditional "pivote" position.