Though, so long as we're looking at evidence, if we take Quirrell at his word, then his ability to cast the spell despite not wanting his opponent dead is pretty strong evidence that the requirement is in fact removed.

Just because he didn't intend to kill him doesn't mean he didn't want him dead. As Moody said, you have to want it, not just for the greater good, but as an end unto itself. Quirrell might have wanted to kill Bahry as an end unto itself, whereas for matters of convenience it was better to leave him alive.