This actually used to be taught to CHP back in the 60’s, when I was taking drivers ed; we had to read the article they published. It cuts reaction times, and therefore stopping distances.
You do NOT keep a foot touching, let alone riding, the brake; nor do you keep giving it throttle, but it is still measurably quicker to let off the gas while the other foot is hitting the brake, than it is to transfer the one foot between pedals.
Most of the time, though I had a stick, and was doing toe-heel down-shifts, while braking, prior to drifting a turn.
That describes my driving in decades past. I once wore out a set of tires in 8,000 miles. When I tried to collect on the warranty (for 40,000 miles or so), the dealer just laughed.