Defending the first delivery is a solved problem; what happens to the loose ball forty seconds later is not.
The second phase of a corner is where zonal systems actually break
The corner comes in, a defender wins the header, and the ball goes twelve yards out to the edge of the box. Everybody exhales. Nothing has been resolved.
What follows is the least organised forty seconds in football. The zone has done its job and the zone is now obsolete, because the players in it are set up to defend a ball arriving from the corner flag, and the next ball will arrive from somewhere else entirely. A cross from the edge of the box, a low ball to the near post, a cutback from the byline after a scramble. Different angle, different flight, and the six defenders standing shoulder to shoulder on the six yard line are all facing the wrong way.
Attacking coaches have spent the last few years working exactly here. That is where the rehearsed routines actually pay, not on the first delivery. Leave a player on the edge, win the header deliberately backwards rather than forwards, and attack the space the defence has just vacated as it steps out to clear.
Defending it properly needs a rule that almost nobody states clearly. As the first ball is cleared, who steps and who holds? A zonal setup has no natural answer, because zones are defined relative to the goal for a delivery that has already happened. Man-marking, whatever else is wrong with it, at least survives the transition, because your man is still your man when the ball comes back in.
This is the strongest practical argument for hybrid schemes that I know, and it is not the one usually given. It is not about winning the first header. It is that a couple of man-markers give you continuity when the picture changes and the zone dissolves.
The other option is to be brutal about it and clear the ball out of the stadium, which coaches hate because it hands possession back and starts the loop again, and which wins more games than they admit.
Watch the next set piece goal you see closely. Count the touches between the corner being taken and the ball crossing the line. If it is more than three, the zone was fine, and what failed was the thing after the zone that nobody has a name for.

