Tbf, I don't think we concede many (or certainly haven't in recent seasons) from corners, so I understand the having 11 players back in our box, as generally, it works. It is frustrating at times that we don't leave anyone up as, like we've seen ourselves all to often this season, the quick break can be deadly, but there are bigger issues wrt corners, both defensively and offensively.
An opposite argument would be leaving one, two or even three maybe up field would force the opposition to bring some back, which frees up space in the box for defenders and goalie to move. Also the attacker, but I'd say that would favour the defending team more.
I don't think you can blame Martinez or Moyes for players not beating the first man. For me, that is solely where the players need to take responsibility and vary it/get something in the box, rather than aiming for that tiny perfect gap between 1st man and keeper.