So, "If you make people's life better, more people will want a better life ?"

No, because this formulation assumes we're starting with a fixed number of homeless people whose lives we're only making better. This is erroneous on two grounds: 1) it's not obvious that it makes their lives better in the long run, if it means they're less motivated to personally improve; 2) but second, and more important, the number of people who "need" these services is not fixed and policy can create more of them.

Isn’t that just a rehash of “tragedy of the commons”?

Tragedy of the commons comes from a lack of regulation. Put all the regulation you want, but make sure to guarantee your people live by a humane standard.

If San Francisco is handing out free homes to all who come, how would that not be a tragedy of the commons situation? “Everyone can come to SF to live by a humane standard” will never work.

So what regulations did you have in mind?

Why does the regulations have to be limited to San Francisco ?

You can't have it both ways, with freedom of travel between states and no federal intervention ever into how social policies are applied.

Ok, I totally agree with that. We will never be able to solve the “how can anyone who wants to live in SF do so humanely” problem but we have a shot of doing it in a region with limited immigration (or humane is applied to legal residents only), like Singapore or Finland.