The choice between Pi vs. Tau is completely arbitrary and should be based on minimizing the friction of use. Everyone knows Pi, few knows about Tau. I see no point in spending any more energy than that on this kind of nonsense decisions.
It's more or less just a re-statement of the question.
And it's wrong: we haven't always driven on that side of the road.
We don't always drive on that side now; it depends on where in the world we find ourselves.
Left versus right is symmetric: there is no inherent advantage. Both choices have exactly the same advantages and disadvantages, just with "left" and "right" swapped.
Whether or not to include a factor of two isn't symmetric in this way.
For example, one could make an argument that oral and written communication in the United States would be more efficient if everyone was forced to communicate in Klingon. But the switching cost would be so astronomically high that any possible gains pale in comparison.
(I'm not saying the pi/tau cost/benefit is comparable to English/Klingon, I'm just pointing out that "that's the way we've always done it" is in fact a perfectly legitimate argument. The onus is on the person proposing a change to show that the change is worth it.)
But it is. For the pi/tau thing, it's better if the whole world uses one set of formulas. For the guy who pointed to which side of the road we drive on, it's best if we all agree to drive on the same side. And for units, it's best if we all agree to measure things using the same units - otherwise probes crash into mars and such. All of those are arbitrary decisions and we're better of just sticking with them - except the units one, by using SI units a lot of formulas simplify and arbitrary constants go away. I'm not so sure tau/pi have a similar advantage. If you do change, you'll put the world in a weird transition phase until the change is widespread and that causes problems until it's resolve. Also, with mathematics you have existing and historical papers that use pi, so what to do about those? The legacy of pi would be around a long long time.
It's just like that xkcd comic about introducing a new standard and now having N+1 standards. Except in this case the new standard offers only a factor of two.
See my other comments on this thread about sigma, for instance.
You can argue that you're so used to right triangles that it's the square and the rectangle that should be considered special, and "twice the area" - but I don't think that makes much sense.
Pi is a useful constant, but it's chief role is in cycles/frequencies and circles. Not half-circles. It is perfectly ok to disagree - but I'm one of those people to find the concepts behind pi start making much more sense when thinking of tau as the constant, and half-tau (pi) as the special case.
Maybe it's because I always hate having logic and math concepts waved away as "that's the way it is" when there obviously is some pattern or explanation that's being hidden or lost. I'm no good at rote calculation, and with tau a lot of things that just look odd and "special" unify quite nicely.
It may very well be that for higher dimensions than two (or three) tau doesn't make much more sense than pi - but I found the "tau manifesto" examples plenty convincing.
It was easier for me to grasp, and I believe it would be a lot easier to teach.
As far as I know, that's the extent of the popularity - you can make pies on Pi Day. Again, I'm assuming the Tau day thing is a bit of deadpan, but otherwise it seems to me to be that simple.
Isn't that what the proponents of Tau also argue for?