Now, except perhaps for school exercises, anything complicated is done with a computer and this advantage is much less important.

The increased accuracy and simpler formulas in other places when measuring angles in cycles a.k.a. turns vastly outweigh the advantage of radians for differentiation.

In real applications you almost always compute the derivative of sin(a*x), not of sin(x), so you have to carry a multiplicative constant through derivations anyway and the single advantage of the radian vanishes.