Note that homelessness is a constant flow of people. The services and compulsion removing people from the streets is currently happening. The problem is that the housing market is dumping more new homeless onto the street than our current system can handle. Turning off the faucet, so to speak, will make dealing with the existing homeless population a much simpler and more humane activity.

If you redefine "homelessness" to only include those with addiction or mental illness problems, then you might have a point. But that's not a terrible useful definition, and many of those addiction and mental illness problems stem from not having housing and the extreme difficulty of that situation.

Other areas with higher rates of addiction, but cheaper housing, have lower rates of homelessness. Cheaper housing really does allow people to get off the streets.

Expensive housing is also correlated with better provisioning of services which draws people here.

I am not redefining anything, I am describing to you what people are colloquially talking about and why these conversations oftentimes are just people talking past each other because they have different issues in mind. When people in SF say "homelessness is out of control", they are typically talking about the population I am mentioning - one that is unlikely to be helped by changes to housing costs at the margin.