Can’t believe I’m still trying to explain this for the hard of understanding: Footbrakes are not operated by an on/off switch. There are various degrees of modulation. Should the driver’s foot be a bit heavy on the brake and loss of traction occurs, the average none-racetrack-trained driver will find it easier to comprehend what’s happening and the best course of action to take than they would if they lose traction due to a bodged downchange/heel & toe.
Also, if you’re going to argue, at least stick to the same set of parameters for each type of braking. You’re using engine braking down a hill as an example of why using the footbrake on icy roads is a bad idea.
Anti-trolling – severe/bodged engine braking won’t lock the wheels, it’ll just cause them rotate slower than necessary to maintain traction.
EDIT:
even a very light application of the brakes will cause the wheels to lock
Really? I mean, really really? You come across as someone who knows about cars and driving and all that, but… really?