Good sir,
One can only suggest that we should agree to disagree.
The whole Industry is based on probabilities - in general, there are few certainties, if any, about aircraft. That's the nature of distribution curves and probabilities of failure.
with 6000 feet ahead gives me the choice of stopping a rolling aircraft with twice my landing distance ahead
Of course it does.
Now, whether such a decision, on a routine basis, is sound or not is a matter for standardisation debate.
As an aside, what do you do in the case where you have, say, 300 - 400ft spare pad in front at V1 with tiger country in the overrun ?