My Janome 7700 has a very large throat--over 11" they say and I did a King on it without any problems on it in April. I must say that using a thinner batting made a world of difference as opposed to a thicker batting (poly)....with a thicker poly batting, there simply wouldn't have been room.
But the average cotton batting is quite thin--thinner even than the thin poly one I used--so for people using cotton, doing a King on a Janome 7700 or newer, shouldn't be a big problem with space.