Every time I hear "The problem with zonal marking is..." I just cringe. It's lazy criticism. Lots of teams mark zonally and barely concede from set pieces. But one team does it and concedes and suddenly the whole system is s***.
Yes, a zonal system can result in players not marking players. But you can't use a man system if you have a small team. For that matter, man marking systems can draw players out of position. So if a team doesn't use either system correctly there'll always be a free man in a penalty area.
Personally I think there should be a mixture of the two, you put your best defenders on the biggest threats, then the rest mark zonally. Which is what most good teams do anyway.
Indeed, you put players in the zones and then put your big men on their big men.