Thus when one wheel hits a patch of ice just as you roll up to a stop sign, the brakes on the other three wheels release and you skitter into the intersection, because God forbid that one wheel should skid a little.
That's a cheap/poor ABS system. A decent system is a "4-channel" where each tire is monitored and managed independently.
A friend of mine races cars in varying degrees of modification and I asked about ABS in racing once. He says there is no way at all for any human to modulate brake pressure as well as a decent ABS system, but that since he's "driving way ahead of where the car is" he can win by not using ABS - he can anticipate what the situation will be and not just what it is. So he races without ABS, but off the track he always has it on.
Short stopping distances is only one goal for ABS. Control under max braking is just as important: if the wheels lock up the car will spin if there's even the slightest angular momentum at the start.