re: More light doesn't mean less burglary
You make a good point that there is a lot more to crime than burglary.
The rest is not an easy problem to analyze. Almost by definition, well-lit areas also tend to be more public and have more people in them, so it's hard to pick out lighting from other factors.
It does go without saying that it's a lot harder to sneak up on or ambush somebody in a well-lit area, which gives your daughter a better chance to perform an amateur colonoscopy on some thug with that chair leg. A gun would be better--more range--but a baton with a nice taser attachment wouldn't suck either.