There is an additional problem
Ice builds up on ice which is already there faster than on clean surfaces. If you polish frost, you may actually be able to fly, BUT there is now a layer of ice where the anti-icing can't get at it, and where ice can now build up when on a properly de-iced surface, it wouldn't.
Do your de-icing properly, and watch your holdover times! Accept no substitute.
OORW