i love radians and get the appeal, but i feel like in terms of learning / empirical applications like game math, we missed by not having a unit of rotation which is 1 unit per circle.
a right angle is 1 / 4 (thing)
facing backward is heading += 1/2 (thing)
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In computer languages like Frink and Beads You have physical units of measurement, and one of the units for angle is revolutions which is what you are advocating for. Also supports gradians and radians and degrees. so 180 deg == pi rad == 0.5 rev.
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that always seemed like such a neat feature. i've never worked in a language which had that.
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I do like it when angles can be checked in these systems - some of the follow SI units more strictly, treating angles to be dimensionless ratios. 😔