I agree that the immediate risk of death would probably influence it a bit. On the other hand, it's pretty clear that there is not a strong negative correlation

I agree that the immediate risk of death would probably influence it a bit. On the other hand, it's pretty clear that there is not a strong negative correlation between "risk of death" and "crime rate" in the world, just think about south America (high death risk and high crime) and the Nordic countries (low death risk low crime). I also strongly disagree with the statement "It's the fact that a jail/prison sentence is meaningless to most criminals (if they're even sent there), that we have such rampant crime.". Again, compare prison sentences in the USA with e.g Norway, then compare their recidivism rates. There are many many factors that play into crime rate (poverty, education, and recidivism being important ones), reducing it to 'our prisons are too nice' is way too simple.