>The result was a disaster.

wtf? metres and centimetres are not different types! they are just different ways of writing same type: Length. radians and degrees are just ways of writing a dimensionless Angle quantity. you made the absolutely elementary mistake of conflating a physical quantity with the unit used to measure it, of course it was a disaster.

>nothing sensible to infer when you, say, multiply an angle and a distance

angles are dimensionless so they should just be a distinct type of float. there is literally no problem here.