ABS helps just about anyone stop faster.

It prevents the wheels from locking up and skidding, which is too easy to do. If you ever see a graph of braking force vs. pedal pressure of ABS vs. non-ABS cars, they both have a rising rate up to a peak. The ABS-equipped car will peak have a small spike, then drop to a value of about 90% of that, at which it will plateau, no matter how much pedal pressure is applied. The non-ABS car will peak at the same spike, then see a drastic plummet as more pedal pressure is applied, since the wheels begin skidding at that peak. The ABS car senses the wheels just starting to slip at that peak, which initiates force suppression.

So theoretically, if you've got the JDM Stage 6 driver mod and all achievements unlocked, you could "plateau" your braking curve at a point higher than 90% of the absolute limit, in that small (tiny) window between ABS braking at the maximum limit of adhesion. Now until I personally datalog braking force before and after and ABS install, with all other things being equal, I'm going to assume pretty much nobody is going to be able to have such precise brake throttling (oxy moron, I know) to constantly hold braking pressure above that ABS plateau.

Another thing is consistency. I would think it would be much easier to control a car that is undergoing constant braking force, rather than teetering near the limits as the driver is trying to hold his foot steady, or increase/decrease pedal pressure smoothly. On top of that, it would be much easier to control the car when you can simply plant your left foot (or right toe, pro), and focus on the gas, clutch, steering, other cars, pedestrians, gunfire, road head, whatever. Here's another consistency factor: get a little overzealous or panicky just once and you could flat-spot the tires enough to put a damper on all performance aspects.

On top of this, I can only imagine where ABS systems have gone since I've become familiar with this basic advantage. Improved sensors, dedicated control units, better valving, etc.