I argued this idea to a couple of my classmates when I was a physics undergrad, and they agreed. However, I later changed opinions because of what this does to the derivatives/integrals of your trig functions.

For general periodic functions, [0, 1) is a good domain. But circles and spheres are geometric objects, and radians/steradians are geometrically significant units that are well suited for general purposes.

I do remember that Doom uses an interesting alternative representation where an angle is a u16 multiple of `(2 * pi) / 65536`. Fixed point is sometimes a good choice in games and simulations due to having uniform precision.