Here is my take on it. A (the) key element in Pep's tactic is to put pressure on the opponents. When we have lost the ball we attack them to get it back ASAP, and when we have the ball we move it forward and around quickly, so the opposing team can never relax. The high possession rate is a consequence of the high energy pressing, not a goal in itself.
The defense is key in keeping this pressure up on the opposing team, because as soon as we win the ball we have to attack. Therefore Pep wanted Stones, and therefore he wants Bravo. Surely Joe and Willy can also pass the ball to one of our players. Willy is giving it a good go as far as I am concerned. But those who cannot see that Bravo is able to do this passing quicker, sharper and more precise, well they do not want to see it. Bravo is exactly the 11th field player Pep needs to implement his high energy pressure play. Only Neuer would be better, but we can't get him.
Getting Bravo will enable our team to shift the pressing up one gear when switching from defending to attacking, and thus make us more of a Pep team.