A back line can only step up as far as the man behind it is prepared to come off his line to cover.
How high a defence plays is set by the keeper's feet, not the centre backs
Thirty yards from goal, sometimes more, standing on the edge of the centre circle while his defence squeezes play into the opposition half. That is where a goalkeeper in a high-line side spends a large part of the match, and the distance he is willing to stand from his own goal is the actual constraint on how far up the pitch his defenders can play.
The arithmetic is simple enough. A defensive line pushed to the halfway line leaves an enormous space behind it, and that space cannot be defended by defenders, who are facing the wrong way and will be running from a standing start against a forward already moving. It can only be defended by a goalkeeper starting high, reading the pass early and getting to the ball first. If he is not comfortable doing that, the line has to drop, whatever the coach has drawn on the board.
Which makes the goalkeeper the most tactically load-bearing player in this kind of team, and it explains why so many sides changed keepers when they changed their approach. It is not really about playing out from the back, though that gets the attention. It is about a man who will sprint twenty-five yards to head a ball away near the touchline, and who accepts that when he misjudges one, the highlight will follow him for a season.
The risk is asymmetric in a cruel way. A goalkeeper who comes and clears successfully sixty times a season gets no credit at all, because the danger never materialised and nobody remembers a ball headed clear at the halfway line. The one time he misjudges it, the ball rolls into an empty net and the clip is played until he retires. Rational self-interest points every keeper toward staying at home.
So when a team's line drops fifteen yards over the course of a season and the pressing numbers decay with it, I do not immediately look at the centre backs' recovery pace. I look at whether the keeper has had one bad moment recently and started, entirely humanly, to hedge.
Fix the keeper's confidence and the line goes back up by itself. Nobody has to say a word about it.

