The elegant bear in the tuxedo knows what's up. Converting between radians and degrees is the mathematical equivalent of choosing between metric and imperial units—except one makes you look sophisticated and the other gets your spacecraft crashed into Mars.
For the uninitiated: Planck's constant (ℏ) divided by 2π gives you the reduced Planck constant in radians. Divide by 360 instead, and you've just committed the cardinal sin of using degree mode on your calculator during a physics exam. Your professor can smell this mistake from three classrooms away.