Desire is not a hindrance.. attachment/addiction to objects of desire is. And this is, in fact, the proper translation of Tanha. (Craving isn't a bad one either, as long as it is in the sense of a habitual craving).

The translation made that "Suffering arises from desire" has caused more difficulty than has helped, in my view. The modern translation has been, for some time, "Suffering arises from attachment".

This is because it is not possible to rid yourself of desire. Ever. You are human. You will always desire things. What you CAN rid yourself of is attachment to those desires.

To answer your question, renunciation of everything except The Path, and thus being subject to attachment TO The Path, is considered easier than the alternative, and is thus thought to be a more expedient way to reach enlightenment by some schools.