I can see the utility in programming, since defining Tau to be 2 * pi potentially saves a lot of multiplication operations (although a good compiler would optimize these away anyway).
But I agree that it's a distraction, and I don't think the radial relationship is that important. I got over my annoyance of typing 2 * pi by thinking about it as the ratio of the diameter to the circumference.
I neither know nor care. It doesn't make geometry any more difficult to conceive of it that way, so I've been happy to do so. I do a lot of compass & straightedge type geometry for fun so it wasn't hard to adapt.
I disagree, but setting aside the radius/diameter debate, consider the simple equation: area=pir^2. How is it not more difficult to think of the constant in terms of diameter, when the rest of your equation is in terms of the radius. Unless you use area = 1/4pi*d^2, which I have never seen.
I'm not telling you what to do, I'm telling you what I like to do. Yes, I do sometimes use (pi * d^2)/4. It's not more efficient, and I didn't claim it was (though if I were concerned with efficiency I could argue that pi * d is a pleasingly simple way to calculate circumference).
I'm sorry that my personal idiosyncrasy bothers you so much.
But I agree that it's a distraction, and I don't think the radial relationship is that important. I got over my annoyance of typing 2 * pi by thinking about it as the ratio of the diameter to the circumference.