The major motivation for radians is arc length parametrization, really. Meaning that in a circle of radius 1 unit (in whatever measurement unit you've chosen),

The major motivation for radians is arc length parametrization, really. Meaning that in a circle of radius 1 unit (in whatever measurement unit you've chosen), an arc formed by a k-rad angle measures k units. There is an intentional coincidence of angles and arc measurements.