Cars do not brake well in a corner, though modern traction control does a great job of hiding that fact. You can often brake LATER if you brake hard in a straight line to slow the car, then as Alex said, the key is how you come off the brakes. You need to gently roll off the brakes as you turn to the apex AFTER your straight line braking to help with rotation by keeping the front tires loaded appropriately. Riding this edge of traction is also an advanced skill that takes practice to feel that is only getting harder to learn as the modern cars hide this limit by cutting things off way before the limit and dragging only one brake to stop the desired rotation.
One of the main reasons I don't teach much anymore is that all of these technique and results can be demonstrated and learned in a old 911 or 944 or Miata, but I have no idea how to even begin to teach that stuff to a computer controlled GT3 or any other new Porsche. New systems work so smoothly, new drivers have no idea the cars is driving, not them. Even with traction control "off" it usually kicks in when you touch the brakes and I certainly can't keep track from year to year and model to model if you can turn it off, how much, and what mode is best as Porsche really does not want you to know the truth about all that.
I think the best reason to teach some of this stuff is to build excitement to keep drivers coming back, not to improve lap times or make them safer.
Jad, you are exactly right. And I disagree with you.
I teach trail braking because my students aren't always going to be driving their new(ish) Porsche. They may be driving a rented box truck on a snowy mountain road when they move to Colorado, or out for a foolish romp in their buddy's hot rod '64 Falcon, or take a few laps in their other buddy's 3.2 Carrera. They may ride their motorcycle up to Julian. They may get in a hurry on a fork lift (don't laugh, trail braking works on
everything).
We should be teaching works-in-anything driving techniques, not just Porsche specific driving techniques.
When I learned to fly 30+ years ago, my instructor insisted that we take as different an airplane as we could find for every lesson. Six seat transportation airplanes, feeble powered tube'n fabric tail draggers, big HP aerobatic monsters, high wing, low wing, twin engines, retractable gear, gliders, etc. I flew into small airports, huge airports, farmers fields, dry lakes in the desert, and landed on concrete, asphalt, dirt, grass, runways long/wide, very short/narrow, you name it.
It was great training, by the time I got my license I had the confidence and experience to fly anything, anywhere.
As much as possible we should do the same for our 4 wheel students, not just teach them to fly "one plane".