You assume that police quickly showing up save lives (except only for swatting). This might be true in some cases, like mass shootings.
But in case of domestic disputes it's not that clear cut. Police arrives in minutes, in the heat of the moment, escalate further and they shoot someone, usually the best armed one among people arguing or just the one that has most trouble with calming immediately in the middle of a quarrel. In many cases if they caught a flat tire along the way and arrived 10 minutes later, situation might deescalate till then.
There must be some optimal reaction time for the police otherwise if faster is always better then the best thing would be to each of us having a policemen with loaded gun pointed at the back of our head all the time, half-asleep, ready to be woken up to shoot immediately in reaction to whatever crime we seem to be trying to commit.
But in case of domestic disputes it's not that clear cut. Police arrives in minutes, in the heat of the moment, escalate further and they shoot someone, usually the best armed one among people arguing or just the one that has most trouble with calming immediately in the middle of a quarrel. In many cases if they caught a flat tire along the way and arrived 10 minutes later, situation might deescalate till then.
There must be some optimal reaction time for the police otherwise if faster is always better then the best thing would be to each of us having a policemen with loaded gun pointed at the back of our head all the time, half-asleep, ready to be woken up to shoot immediately in reaction to whatever crime we seem to be trying to commit.