Your argument is like saying hospitals obviously make people sick instead of treating illness because there are so many sick people in hospitals.
One of the main causes cited in "Seattle is Dying" for the surge in homelessness is that it's become known as a good place to go if your poor.
There are two reasons for this, the first is that your chance of escaping poverty in Seattle and the other 'liberal' cities you've mentioned is 2 to 3 times better than in traditional republican strongholds. I don't think helping people escape poverty is a goal worthy of criticism.
The tricky part of programs that help people escape poverty is that they can be taken advantage of by those who have no desire to escape poverty and just want to take advantage of that system. I would agree that preventing these people from abusing the system requires continuous vigilance to prevent this, but I don't think that even these liberal cities fail to recognize that.
My retired dad volunteers at a drop-in center for the poor and homeless, funded by the same programs you're suggesting are part of the problem. It's very much the prototypical bleeding heart liberal sort of place, yet they have impressively little tolerance for those just looking to take advantage of the system. People who need and want help, and who are looking to improve their situation have access to various forms of assistance, those who don't are prohibited from even going inside the drop-in center, there's certainly no coddling of those who aren't interested in bettering their situation.