In terms of crosses fired over, I think you're right, although even well organised defences make mistakes and disorganised ones make more.
But given how much Pep values possession, I can't see the sense in lumping it in and "hoping" and probably having a 50% chance of losing the ball. Surely we'd be better off passing it short and drawing the opposition out so we can open up gaps and try to develop things that way. Just lumping it across seems about as "non-Pep-like" as the keeper hoofing it up field.