As a third hand for your rappel, a toothed ascender seems like a bad idea. Petzl makes another device called the Shunt which is more suitable to third hand use. Although in the case of icy ropes, maybe teeth are a hard requirement.
The Shunt is great, but there are some potentially dangerous gotchas in its operation. Never use it with ropes of different diameter. As a rappel backup, the shunt can fail if you place it above your belay device. The risk is that a panicked operator will hold the device open. In the correct mode of operation, you place the shunt below your belay device. If you're disabled, the shunt will lock off. If you panic and hold it open, the force you apply to the device will arrest your rappel.
Yes, it's applications are very specialized, this is true.
I've only used ascenders when climbing up free hanging rope, and they work very well for that purpose (I've done several hundred meters of vertical ascent in a single trip using this technique).