Forget the statistics, the Olympic gold, the Stanley Cups, even the Vezinas.
Dominik Hasek is the best of all time is because of his ability to implode the minds of his opponents.
Everything Hasek did, every movement, was organized around a singular purpose: the save. It was an instinctive reaction from a being who had seemingly evolved solely to stop pucks. Every motion felt like act of apparent desperation, like a mother protecting her cubs. No resource went untapped - legs, arms, skates, sticks, and faces were all willingly employed.
The sheer savageness of Hasek's ability was mind-melting. Opponents often became frustrated, feeling like they had beat him only to be ruthlessly rejected. This was fully evident during the 1998 Winter Olympics versus Canada. You could sense the trepidation among Canadian shooters, culminating in Eric Lindros' shootout attempt. Lindros needed perfection, but he knew that perfection may not be enough. Even at his absolute best, confidence began to erode, and however slight it may have been, it was enough - the matchup had already swung in Hasek's favour.
That was the Dominator's ultimate talent: the ability to weaken the other team's emotional strength. Teams would see him warming up, and at that moment just the tiniest modicum of doubt would manifest itself. As the game progressed, he would feed that doubt, eating away the professional veneer of confidence.
Domink Hasek is the best of all time because he could affect the game like no other goaltender before or since.