Almost all the holding power of a good screw comes from the outer threads of the screw (closer to the hanger).  Moreso, the actual thread length on 13 cm and 22 cm is pretty similar (or identical i think).  Your statement is only true if the surface ice is bad, but the underlying ice is decent.  Even then, you could clear the surface ice.  On a mixed alpine climb where the choice was between one screw and zero, you are far more likely to find thin ice <13 cm vs >22cm.  In that situation, the completely driven 13cm screw is much stronger than a half driven 22cm screw.