The drilled holes aren't always perfectly centered. For single sides boards this doesn't make much difference, but for plated through holes having a hole in the pads copper could mean that the pad only partly connects to the through-hole metalization if the drill doesn't match the hole perfectly.
Are through-hole pads without hole in the copper allowed?
edit
About the larger annular ring (re Leon's comment): it's not the outside I'm worried about. I've never had an annular ring so small that the drill comes outside of it. If the drill goes a little bit to the west, then possibly on the east side the copper of my pad doesn't connect to the through-hole metalization. This wouldn't be noticed when the board is tested, since there's still a (partial) connection, but it may have a higher resistance.
Best Answer
I understand what you want, but it doesn't make sense: the drill diameter is determined by the hole diameter in your pad. No hole in the pad = no hole drilled.