I agree that this makes sense for the kind of situations that the article talks about. If you only need to express common angles like 90 degrees, 45 and so on, radians are just messy (though in physics, you get used to it).

But in other cases, radians are useful. For example consider the case of small deviations from a direction. If you give it in radians, let's say three mrad (milliradians), it's very easy to estimate how large the error will be over the course of a meter; three mm.

This is just to say: choose the right unit for the job.