In cars that have ABS and traction control, it is usually possible to turn the TC off, but not the ABS. So that limits your choices, but I’d prefer it that way than the other way 'round.
Traction control: For rank newbies, I recommend they leave it on for the first few sessions, but turn it off after they have some track time under their belts. The only exception is if it is raining, when I’ll leave it on for drivers up to the intermediate level, unless they are especially cautious or skilled.
The problem with traction control is that a new student won’t realize when the system is correcting his mistakes, and will therefore keep making them. In the beginning, when he’s a bit overwhelmed by everything he has to take in, that’s okay. But after he has the line down relatively well and is starting to pick up speed, he needs to know how his inputs affect the car’s handling and what kinds of moves can cause a spin or drift. Then he can avoid them or use them to his benefit. TC masks his mistakes, and even worse, because he probably won’t realize what the system is doing for him, he will have an unrealistic perception of the car’s capabilities and his own skill level. If he tries the same moves in a car without TC, he can get in trouble.
(An advanced driver can tell when the TC is doing the driving instead of him. Once in a while I’ll get halfway through Turn One and realize the car isn’t hanging its rear out the way I told it to. Then it occurs to me: I didn’t turn off the TC before leaving the pits!)
I’ve had students who were scared to turn the TC off, because they were concerned that they might overdrive the car and get into trouble without it. I tried to persuade them that as long as they built up their speed slowly and steadily, they would find the edge of performance without catastrophic results. But at least one student wouldn’t buy that, and kept the TC on all the time. He was one of my most frustrating students.
Another downside of TC is that on some cars (including the 350Z I drive), driving on track with TC on will wear out the rear brake pads faster than the fronts. Ordinarily, the front brakes do most of the stopping, so they are made bigger and the front pads normally wear out first. TC generally works by applying braking to different wheels preferentially to stop a spin or slide; it’s usually the rear brakes that can accomplish that. But since rear brakes are smaller, they can overheat more easily and the pads will wear faster.
ABS: Your experience points out the benefits and pitfalls of ABS in track driving. It sure makes teaching easier. You can just say, “BRAKE HARD!” and not worry about the student locking up or flat-spotting the tires. And if he plans to remain in a street car with ABS, that’s okay.
Except that he doesn’t learn the important skill of threshold braking. So if he gets into a car without ABS, he’ll have to learn. Not impossible, although, as you found, it takes some time. But if he’s already mastered the other elements of track driving–the line, shifting, etc.–picking up threshold braking won’t be too hard.
So ABS delays the learning of a skill that, much like manual shifting (in street driving), is useful, but not always necessary, and that is easier for an experienced driver to learn than a newbie who may well be overwhelmed with everything else he’s trying to absorb.
Finally, it is possible to learn threshold braking in an ABS car. It’s usually not hard to tell when the ABS kicks in: there’s a throbbing in the pedal as it pulsates on and off. So you have the student try to brake as hard as he can without activating the ABS, much he would in a non-ABS car. This won’t result in the shortest stopping distance, since the ABS can outperform any human driver, but it will teach the skill in a way that can be applied (if somewhat imperfectly) to non-ABS cars.
