What reasoning do you have to support being remorseful for saving others from a clear and present danger?
This isn't an answer to the question. It is in fact a non-answer that endorses the irrational as an enlightened state.
Edit: and I think remorse is a healthy and useful check on the excess of police violence we've been seeing. I suppose if you think it's all just fine, we're not going to have much common ground for understanding.
Your problem is not with the definition, but in that the definition doesn't match the situation.
Another pattern we see a lot of is cops escalating situations, and then when the accused (rather understandably) matches that escalation, then the officer kills and claims self defense. I'd actually describe that as premeditated murder, because the danger is a predictable result of the cop's own actions.
In the very rare instance of an emplaced shooter, where less lethal means cannot be used and the area cannot be evacuated, then yeah, it makes sense to shoot back defensively.
Way too much of police training is focused on killing people. Training, as is done in much of the world, should focus on de-escalation.
More cops die in traffic than at the hands of criminals. It's an astonishingly safe job, considering the focus placed on "remorseless killing".