> taxpayer funded

I don't understand the reflexive nature many people present in jumping this kind of framing. Of course it's taxpayer funded. Everything is taxpayer funded. Even when it's not literally paid from taxes collected by the government, it's probably funded by people who pay taxes.

The price you pay for your groceries funds not just the wholesale purchase of the goods you pay for but also the labor, facilities, equipment and resources used to purchase, deliver, store and sell those goods. Considering the total amount of taxes collected versus the revenue of the place you get your groceries, you probably contribute more of your income to operating that place than to any single service funded directly from taxes. The amount of those grocery expenses that goes directly into profits alone is probably still greater than that. Housing first specifically also literally is cheaper than the previous approach by reducing expenses for medical services, policing and incarceration.

So "taxpayer funded" is neither a meaningful qualifier if taken literally nor do its implications stand up to scrutiny.

The most common reason for using this phrase is an emotional appeal to selfishness. Your money is being spent without your say on services you don't benefit from. I find that framing morally appalling but even so, what is the alternative? What the US did before was more expensive. Not housing people means more health issues and ER visits. Throwing them in prison means housing and feeding them at a massive multiple of the cost of a housing first initiative. If you want to save costs without spending money on housing, I guess you could cut their access to medical services but then you might as well allow law enforcement to shoot them on sight as the outcome will be the same.

> On the other hand, that housing given to someone who is capable of navigating welfare bureaucracy on their own

What you're describing is triage, not housing the homeless. If your housing program is small enough that you have to engage in triage and turn people away, it's not addressing homelessness, it's addressing a fraction of the homeless population. It's better than nothing, sure, but it's not enough.

Also triage means weighing the necessary resources for treatment against the likelihood of recovery and the likely extent of the recovery. You don't treat someone who can walk it off but you also don't treat someone who's in very poor health or too far gone to be saved without using a disproportionate amount of resources.

Triage is not how you organize a hospital. Triage is how you respond to an overwhelming emergency situation without access to necessary resources. Triage is a last resort measure to reduce the number of people who will die, not a strategy for helping people survive and thrive.

Homelessness is not a natural disaster, not a spontaneous pandemic. Homelessness is a longstanding social issue most often directly arising from poverty and lack of mental health support. If your concern is with the support being wasted on people with worse chances and not support being insufficiently funded for that kind of decision not having to be made, I think you might be overestimating your humanitarianism.