There is no benefit to not using it.
Hmm, but why is there no benefit? It saves a turn and resources.
In my opinion, the Pit in Tower is useless and not intended for use in its current form.
Especially considering that Tower mostly plays a rush strategy, getting 2-3 Fury units won't offset any losses, and in a longer game, an extra 10-12 Fury units won't really make a difference either.