I'm so glad someone else finally said this. This article takes the approach of simplicity of code, which I do agree with, but additionally I've been thinking turns would have to be more intuitive and easier to teach (particularly to disinterested teenagers) for YEARS, and I finally feel vindicated at least one person agrees with me.
Turns are really the most neutral way to count an angle. We don't use them for everyday physical things because the numbers we'd deal with would be too small to work well for feeble human minds, hence degrees. But for the mathematical world where we currently use radians, turns make so much more sense.