Revolutions are counted be higher values than ##2 \pi##.
Radians is a derived (from a circle with radius one meter) SI unit, which doesn't mean it cannot be a dimensionless number, because it is the ratio of two lengths, and ##\frac{m}{m}=1##. It simply means, we are allowed to write ##1 \operatorname{rad}##, in contrast to e.g. ##1 \operatorname{Oz}##. It makes mathematically perfect sense to consider it as a pure number, as in

However, it can also make sense to treat it formally as a unit, e.g. when checking a physical calculation where the angles don't cancel out or in a case like this:

In the end it remains a ratio of two quantities of the same dimension, length. And as such ##1 \operatorname{rad} = 1##.

My point exactly.
We can define angles with respect to either radians, degrees, gradians, grons, or revolutions.
Still, we have to make sure to identify that unit of angle, because otherwise our calculations come to naught.