Part of the prison overcrowding problem is the reluctance of states to use the death penalty due to the ridiculous number of legal challenges to every option for execution available. Someone is sentenced to death under the laws of the state should be put down, not given lifetime incarceration. I'm really surprised you're arguing community outreach and drug diversion for non violent crimes, that is one of the issues that plagues major Metropolitan areas, especially in California. What stops a person from committing crime it there is no punishment that makes a lasting impression?
A hundred pound woman protecting herself from a rapist, really? Provided she has enough awareness of the impending crime to draw a firearm and use it to protect herself, what will she do if the criminal also had a gun and disabled her first? You speak of overwhelming force as a means of diversion, but that is only effective so long as it can be deployed effectively. We play a game with very effective ambush mechanics, people employ the same subterfuge or stalking to keep their victims unaware before they strike. A gun out of hand is no use at all, and just as likely it's going to wind up in the possession of the assailant.
A society where criminals are locked up, those who are reformed actually reformed, and the fear of retribution so great that non mentally imbalanced people will think twice. That is an ideal society. Ours is suffering from drug addiction, overtly generous welfare benefits going beyond basic food, shelter and health-care, and a system of justice being neutered by the privileged few who don't understand what a bane free roaming, gun toting recitivists are.