Because violent felonies such as homicide proximity is the requisite factor in victimhood. ie The victim must be located near the killer.

Given 1 homicide in 100k for 100sq miles called "rural" vs 1 homicide in 100k for 5 sq miles called "urban", your odds of being in proximity of a homicide are much higher in the urban area. 20 times more likely.

I live in lower Manhattan, and there have been many shootings within a mile of me in the past year, even a few within two blocks of me, but because the per-capita numbers are so low, I'm pretty unconcerned about being shot, and so it doesn't really bother that I'm near the shootings. I don't really see how standardizing by (people * area) does you any good in capturing public safety, or even perceived public safety

Being further away from killers that I'm equally likely to be victims of isn't any more comforting.

> Because violent felonies such as homicide proximity is the requisite factor in victimhood

This doesn't stand up. Crime statistics are measured after the crimes happen; whatever effect might be due to proximity has already taken place.

Consider: in your example you say two places have equal per-capita homicide rates but one is 20x denser. It follows that the denser area will have 20x more people "in proximity" to any given homicide, and therefore that P(victim|proximity) must be 20x lower compared to the rural place.

The way you've done the math only makes sense if everyone "in proximity" of a homicide was equally likely to be a victim, but given equal per-capita rates that can't be the case.