alt Hacker NewsThe one place where radians are more convenient is when you are at the centre of the circle. Then something which is as wide (or tall) as it is far away subtends one radian in your view. (And correspondingly, if it subtends half a radian it is half as wide as it is far away, etc.)
This happens to be the most common situation in which I measure angles.
More convenient than degrees. This is unrelated to pi vs tau (using tau or pi doesn't change the meaning of radians, the properties you mention are not affected). What OP is getting at is that the same number of radians, e.g. 1.57 (quarter turn) is more naturally expressed as tau/4 than pi/2.