You can see that if a was equal to g, your downward acceleration is that of gravity, namely the cable has snapped in the elevator, Then you don't feel any weight.
The summer months see Times Square overrun by visitors all scrambling for their "I Heart NYC" t-shirt and matching sun visor, while the Empire State Building's elevator queue can, through the heat-haze, seem to extend as far, horizontally, as the iconic building stretches for the skies.
While that might seem less than instant, it compares favorably with the alternative -- taking the elevator to the seventh floor, finding you car and then driving down endless ramps praying that your alloys don't make contact with the concrete skirts.