That's the whole concept of an ILS - that is so precise that you will not hit anything but the runway.
Hence, the reason that you have to make a go around is that you don't have visual reference to make the flare and the roll out. With CAT2/3 ground equipment, it's so precise that it's acceptable that that you touch the runway during the go around as well.
Assuming of course you made a stabilized approach and made the go around due lack of contact. Making a go around at CAT2 min with full scale deflections is maybe not such a good idea.