Deer, especially BIG deer, don't run blindly through the woods. They take a step or few and stop and look and listen and smell... and then they do it again.
Really? This may be true 11 months out of the year and x% of the time during the rut, BUT this is certainly not an absolute for a mature buck in the rut.
Not only in the chase phase, but also in the seek phase, I have had numerous (I don't know the exact count but more than I could count on two hands) bucks over the years move so stinking fast through an area that if you waited for them to stop......well you would still be waiting.
I don't stop a buck as a rule but I have before and will again if the situation calls for it. Is it possible that is is overused by some hunters? Probably so, but to say to never implement the strategy is just as flawed logic as saying to always do it, at least in my opinion.