Contrary to what other comments have suggested, welfare isn't about being a nice civilized society that doesn't leave people behind. Welfare is a bribe. It's a tribute ("danegeld"[2]) we pay to the poor so they don't burn down the city or murder anyone between them and food/shelter. Arresting that class of people would be more expensive as it still pays for their food and shelter.
Do you really want to give up the cheapest and safest option for defending yourself against the bottom ~quarter of the population? Recent events at Ferguson and Baltimor are warning. Ignoring them is not recommended if you value maintaining your current standard of living.
[1] https://www.youtube.com/watch?v=Zzl4B3mrKQE
[2] https://en.wikipedia.org/wiki/Danegeld
[3] Exact amount and the scope of what is mean by "national defense" is off topic.