Veljko Paunovic’s Chicago Fire use zonal marking on corner kicks, which is often derided by fans as ineffective. It almost came back to bite the Fire against the Montreal Impact before Bastian Schweinsteiger scored a late winner, so I think now is a good time to look at the pros and cons of the Fire using this system.
The main “benefit” of zonal marking is probably the phrase you will hear every time there is a discussion on it: it allows you to “attack the ball instead of reacting to the opponent”.