I'm highly dubious that short swords are ineffective or the least effective weapons.
ScholaGladiatora seem to get their bee in a bonnet about many things which seem to work only for them such as their spear obsession. Remember, HEMA is a cesspit of pet theories and personal rivalries and unsupported theories like this balloon in them.
Short swords persist long into history, weapons that last that long tend to have a viable use. Short swords seem to work well in very close combat and are effective at keeping yourself dragged down and stabbed with a dagger, one of the prime dangers of that sort of fighting (along with having your head stove in by a honking great stone someone threw into the air). Short swords even persisted into the era of white harness and long basilards were common among the Swiss and the katsbalger among the Landsknechts.