I'm hardly an expert in the field, but I'll offer my observations and experiences.
what are the criteria for a good urban campsite?
Access to facilities such as water, power, and public transit. Also, inconspicuous.
And how would that be different from a good campsite in the wilderness?
Mainly the power and public transit access I suppose. These first two answers are based on the premise that not all homeless are jobless and that many have cell phones.
Do social services networks use this kind of matrix to work with the homeless?
Generally speaking I believe the answer is no. Most social services have as their objective getting people into stable living situations. A few recognize that some people simply cannot adapt to society for whatever reason and so try to provide them some minimal shelter and services. They might also provide sleeping bags and other gear on occsaion but genreally prefer not to be seen as promoting homelessness.
Are there elements of backpacking equipment or technique that could improve the situation?
Depends what you mean by improve. A sleeping bag might keep a person warmer and that is an improvement over colder. A tent in an urban area might get a person noticed and "moved along", which might not be an improvement.
It's a complicated situation and one for which I feel there aren't any general, correct solutions. I don't think you meant to suggest there would be.
I think its too easy for something said on an internet forum to sound offensive and that is certainly not my intent. You asked a question and I hope I gave frank, polite, and maybe something-to-think-about answers.
To be safe, I'll stop now.