I was planning to return to my irrational defense of pi today but the new bridge was opening and I was really tired after I walked back, and I had steps to bring closer to perfection and generally stuff to do and I ran out of time and, for what it's worth, damn it's hot.
So, just to recap:
Yes, it is completely reasonable to use tau instead of pi because tau is to radian addition as one is to multiplication. However:
Pi is more fun, being the unit that represents as far as you can go without turning back, being a representative of change in a field otherwise full of static things (zero and one, for example, are identities. They're defined by the fact they do nothing.) Pi radians is literally a 180, and thus it carries with it the idea of radical change.
Pi is more emotionally fulfilling. As a constant that shouldn't really be in use because an objectively better one is out there, pi is like the underdog or plucky hero or whatnot in every sports or competition movie you've ever seen. Pi represents the idea that you don't have to be perfect, sometimes the underdog wins. There's not a lot of that in math.
Adding Pi radians is equivalent to multiplying by negative one. Indeed pi and negative one are intimately linked. Adding π*1/X radians is the same as multiplying by -11/X which makes for a very convenient conversion in the complex unit circle (one half pi radians = the square root of negative one.) Negative one is a number that gets almost no respect (just look at the connotations of negative) and it's nice to see it getting some via pi. Take away pi and you're erasing negative one's tiny bit of respect.
Pi embraces duality. When looking in terms of pi radians, the unit circle runs from negative pi to pi. You can start at zero and move in either direction. Furthermore it shows the symmetry and equality inherent in this movement. Apart from the direction of motion, the two paths are the same. Neither can be said to be better or worse than the other.
Tau, on the other hand, has the unit circle running from 0 to tau. There is no hint of duality or equality or any such thing. And, stating from zero, you end up back where you came from. Instead of symbolizing that multiple paths can lead to your destination, it symbolizes that you'll always end up back at zero. A depressing thought if ever there was one.
The plan was for this to be more thought out, and for it to be on video, and for it to involve pie. Apple. But like I said, tired and out of time.