I think it's worth asking why this is such a polarizing slogan. I think the idea that we'd collapse into anarchy without the police is largely a byproduct of decades of nonstop copaganda with a big dash of racism ("if you get rid of the police *those people* will be able to do whatever they want!").
In my neighborhood, "those people" are mostly white meth-heads, and sharing European ancestry with them doesn't make me feel better about them doing whatever they want.
I agree with the premise that comprehensive mental health programs, drug rehabilitation, and anti-poverty programs could have a significant impact on the amount of crime that occurs. And I think that the majority of people are decent people who wouldn't commit serious crime even if there were not police around. However, I also believe that there are people who would commit violence and other kinds of lawlessness if there were no police around.
-k