What you are truly advocating is removing the right to defend yourselves from violence. You are advocating a society in which bullies prevail over the generally passive and non-violent members of society. You are advocating a society in which individuals live in fear of the actions of ruthless thugs who have no problem committing violence to get what they want.
Access to mental health programs, "social services" and education as you have stated do not change the fact that there are violent people, regardless of what services you attempt to force on them. And yes I say force on them, for most individuals who are violent in nature have absolutely no interest in your social programs. They do not sit around thinking, "If I only had a program to go to to suddenly make me less violent". And one who is court ordered to go to these programs are only doing it so they can maintain their freedom as they ignore or resist change.... or pretend to change just to get through the program and back out on the streets. Ive seen this over and over and over with those forced into alcohol rehabilitation by the courts.
The fact is..... you talk about social programs and education and et al. But that does not change the CULTURE that encourages violence.
B) Being permitted --even encouraged-- to kill people you perceive as violent is "a culture that encourages violence."