All this comedy is wasted on you, isn't it? I wrote that whole bit about MI5 and being deported as a foreign agitator for stirring up trouble at the DSA, and all you want to talk about is automotive braking systems. It's disappointing.
Assume manual transmission. The "proper" method which ADIs try to impose is that when coming to a stop you should apply the parking brake before you shift the transmission into neutral.
Now tell me how you can do that if you have a foot-applied parking brake.
That's not what we're talking about; we're talking about how "they" want you to control a manual transmission car with a handbrake, and how that applies to people with years of experience taking and passing the UK driving test.
As to your question, I assume if you roll up to the test in a Citroen XM or mid-90s Mercedes with a foot-operated parking brake, the examiner would a) dip deep into his or her well of knowledge and apply the "control the vehicle" standard as it is intended, b) refuse to perform the test in dogmatic adherence to the "gotta use the handbrake" theory of vehicle control, or c) fashion a psuedo-handbrake out of available materials (perhaps the bananna he or she was planning to have with lunch) and make the test-taker "use" the bananna/handbrake throughout the test to prove they understand the theory, even though the theory doesn't apply to the car at hand.
At any rate, as a lot of this well-crafted comedy seems to be going right by you, I'll just restate my initial (serious) position, and then I'm giving the thread back to the folks that are taking driving tests soon, and probably don't want to read 3 pages of your pedantry and my foolishness.
My position is it's better to just use the handbrake the way "they" want you to use it on the test so you can pass. I agree that "their" method is not the only method that would meet the standard, but it seems ingrained in the DSA and in the various driving schools, and to try and fight against all of that seems like the more difficult path to success.