- As of yet Unknown.
As of yet, no known Rhyme-o-mancer has been introduced.
The magic of Rhyme-o-mancy may be connected to the underlying mechanics of dance fighting, such that the forces of Rhyme and Rhythm cause units to be more effective in combat. If so, Rhyme-o-mancers could be give increase the bonus units receive for in dance fighting. This would be similar to the bonus that golems created by a Dirtamancer receive when stacked with a dirtamancer, and the "huge" bonus that uncroaked receive when stacked with a Croakamancer.
This bonus could be permenent. A Rhyme-o-mancer might be involved in training units so that they can dance fight. If the RCC had no Rhyme-o-mancer, then that could explain why so few of their units could lead a dance fight. Alternatively, training might increase a unit's dance fight stat, but only work on units with some basic skill.
If their bonus was large enough, it might be worth using Rhyme-o-mancers in actual battle, despite the risk. However, given the shortage of casters, their bonus would have to be large.
It is also possible that they provide out of combat bonuses. Construction, for instance, might proceed faster if the workers dance to a song crafted by a Rhyme-o-mancer for that purpose.