bruce was against using the pit, at all, if im not mistaken. besides, even if he wanted to, he'd have to immediately fly whoever had just died overseas, beat up some ubus, gain access to the members-only pool, etc, etc.
i think it was denny, himself, who deemed the pit's actions as super-healing the body. being just-dead or near-dead was the best time to make use of it, as that is when the body is most hurt ... however, technically, that would not limit its use to someone in a fatal state.