I have allowed them to be added to saves in one game. You make a save and before seeing the result can chose to add a Hid Die to the result to power through the effect.

It worked pretty well, at least in terms of the intended effect. Healing in general became a bit better as it preserved this other resource and it boosted martials a bit - especially at higher levels where save began to become a lot more common.

It was interesting but also happened alongside a number of other changes I worked on.