Well, \tau vs \pi is a question of taste, but 1 vs. \tau (or \pi) is not. Because you don't get rid of these weird constants, because \pi (or \tau) is, as a fact, in the circumference and area of circles and in surface and volume of spheres, and in other places. There jus is a weird constant.

And for APIs, you could reasonably well have turns or radians or degrees or even percentage of turns, whatever -- it depend on the context what is 'better'. What's really missing, I think, is the support of units in programming languages (in the type system) so that you cannot mess up when invoking sin()/cos(), because you would be forced to provide a unit.