Please help, my issue with the tuck rule

[rking]

My problem with the tuck rule is that if you coach your quaterbacks right, they can never fumble.

I am of course talking about the New England vs Oakland playoff game a couple years ago.

It was clear that Tom Brady was not throwing the ball, but moving his arm in a throwing motion and making a pump-fake. Why don't teams coach their quarterbacks to, from the time they take the ball from center on a pass play, as they drop back and survey the field, to the time they actually throw the ball, continuously pump-fake the ball ?
That way they can never fumble. If I understand Mike Pereira's explanation of the tuck rule, than this must be true.
Any thoughts ?