If your natural unit is radians, then you're arguing for tau rather than against it.

How many radians in the circle? Tau

How many in half a circle? Tau / 2

How many in a quarter turn? Tau / 4

Much better than mentally switching from a quarter circle to half a pi.

And if you're using it in calculus, it's more natural to integrate from 0 to Tau than from 0 to 2 Pi.