IMHO it
is unnatural, in the same way that strict use of pull-push steering is. I think they should concentrate more on developing a smooth approach rather than imposing strict rules like this. What if you were braking for a tight downhill hairpin? Would you be expected to get off the brakes and allow the car to surge forward whilst you frantically grab for the low gear?
As has been hinted at on other threads, with skilled use of heel & toe downchanges the whole maneouvre becomes one smooth operation with the downchanges an integral part, ie we can think of the entire process of slowing down as a sinusoidal curve on an imaginary g meter, that goes smoothly back to "zero g" as we commence the turn (though this too can be overlapped if you replace the "rule book" with an understanding of the "friction circle").
If you were driving really smoothly you'd be unable to discern where the gearchanges were on the plot, so it wouldn't really matter when they were done.
And if we were to aim for the ultimate perfection of a steady g level that simply moves around the friction circle through the process of braking, turning and acceleration, then under this regime there would never actually be an opportunity for the downchange at all!
That said, I understand the principle that they are trying to teach you to leave a safety margin between braking and manoeuvring, and having to leave time for a gearchange clearly achieves that, but nonetheless I'd have thought this was more a teaching method suited for "basic" motoring rather than advanced driving.
<Dons tin hat and waits for inevitable flak from IAM members...

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