I don't cover my brakes all the time - in fact, I vary my hand position in order to maintain comfort for as long as possible. I suffer with work related upper limb disorder, so this probably is more important to me than many people.
That said, my ability to maneauvre/stop quickly has been tested on many an occasion and appears to come up to scratch.
I'm not a trained cycling instructor, but I've taught a couple of people to cycle and I've found myself instinctively advising them to cover the brakes - just seems like common sense advice to give an inexperienced cyclist.
These days for me it's not a concious thing.