Having a single job that heals through damage wouldn't work in this game at all.
If it produces as much healing as the other healers but more damage, then it makes the other healers obsolete
If it produces less healing than the other healers, then it becomes useless on fights where that healing is needed. This latter outcome is less likely since damage taken in this game is generally too low, but it'd be a balancing nightmare either way.

However, if every healing job follows this healing through damage model, then this issue disappears.