I think you make a good point about the need for law enforcement in high-crime areas, though I disagree strongly that the only solution to that problem is a police force as currently constituted in the US. I think it's worth pointing out that police often has abysmal clearance rates and response times and often do not provide effective relief from the real problems you outline.
However, what I wanted to raise was this:
> the fact is... violent (fatal and nonfatal) crimes do happen at a much higher rate in poor neighborhoods
I think this statement is worth examining.
We certainly know that poor neighborhoods contact the police more often and that the police arrest more people (and record more crimes) in poor neighborhoods. As I said above, I have ever reason to believe residents of poor neighborhoods suffer crimes more often and that each crime does proportionally greater damage to their lives.
I also think that, as people get access to more resources, they are reasons to believe they are less likely to contact the police in all circumstances. That, of course, is the other way to read the stats you linked about poor neighborhoods contacting police. Police clearance rates are often low and contacting the police rarely directly addresses the harm caused by a crime. Also, because we are most likely to be harmed by people in our social circles, wealthier people are more likely to be harmed by more powerful people. These are all reasons that wealthier victims of crimes might choose not to contact the police and generate statistics about them. It's difficult to point to data about what isn't recorded (of course), but I think the feminist movement has done some great work trying to document how under-reported rapes (and other sexual crimes) are.
I just want to encourage skepticism about the systems through which data is collected. Structural elements strongly bias the data that's collected and, if we're serious about changing the system, I think it's advantageous to be skeptical of every element of the system.