They could have stayed part of Pakistan. It could have been worse. My family is Ahmadi. We left for the US in 1986 right before I was born over this death penalty for apostasy business.

You're referencing poll data and using that to project human behaviour across demographics. Not sure that's good science. Secondly you don't factor in that often capital punishment has majority/plurality support in most nations.

Is country X's incarceration rate not related to the quality of it's legal system and institutions?

To a first approximation, incarceration rate is equal to rate of crimes times percent reported to police times percent of solved cases times prosecution rate times sentence length.

Some of these are bad things, some of these are good, and the last one is ugly.

Starting at the beginning of your equation, is what constitutes a "crime" not defined by the legal system to begin with? Perhaps the US has run wild with their definitions and militaristic enforcement of crimes

Not in the direct manner you seem to be implying.

The article that rayiner posted was in reference to overzealous policing of arbitrary culture based moral offenses (not being islamic). Are many of the laws in the US not overzealous and arbitrarily moral based as well? For instance non violent drug crimes being punished with harsher sentences than violent crimes?