I was searching for an earlier post when I bumped into this delightful thread and read through the entire discussion which was such a pleasure. However, I also noticed that having gone off the thread because I thought, wrongly perhaps, that it was a waste of time writing any more, I think this question you asked remained unanswered - and it is an absolutely vital one to understand Sobers' batting.
I had mentioned it in the thread on Cricketers who have had a lasting impact on how the game is played.
Most batsmen who have an all round aggression by which I mean who will be aggresive towards, pace and spin alike, tend to cut, pull and hook marvellously and jump out to spinners to make good length a bit of a myth. Bradman is the epitome and the greatest example of such aggressive batting.
Sobers is the only, as far as I can think, great aggressive batsman in history who made a mockery of good length but never jumped out of the crease (or almost never).
The only way he could bat like that was to do what you say, to stand still till the last possible movement then with one decisive, and lightning quick, movement of feet and bat dispatch the ball of the front foot or back from a position of rock-solidly-grounded-feet. This style could not have worked without being absolutely certain of the line and length of the ball (to make sure which was the spot in all its three dimensions) where the ball would have to be met. This certainty, in turn, could not be had without waiting till the last moment possible to assess the speed, line and height at which the ball would come. And this waiting till the last possible nano-second was possible only by being absolutely still till then with eyes and mind transfixed at that 5 1/4 inch red orb.