Braking while heel and toeing down the gear box is the only way to go when making progress.
If, say, you're blatting along (on a track) at 120mph, and there's a 40mph hairpin at the end...By your theory, we would be hard on the anchors, slower and slower, then as we get off the brakes to turn in, we select second and accelerate away. Problem is, that with the car practically coasting under the last bit of braking, it would be horrifically off balance, and the effect of engaging 2nd could be disastrous.
On the other hand...brake hard in 5th, and as soon as the revs drop enough to allow 4th to be used, heel and toe down into 4th, while maintaining optimum pressure on the brakes. The engine braking effect by having 4th engage would slow the car better than just the brakes, and by the time you've got to second, you'll have the car nicely set up for the corner, on neutral throttle.
All this is theoretical by my speaking btw, I've never driven on a track before. But it's what every single rally driver does, every car with a manual gearbox on track as well....so it must be right