I realize you say "I'm not suggesting we re-criminalise homelessness"... however in many people's eyes, there's a "but" there that if not suggesting it certainly implies "but we should certainly consider it". To which I say:

We have the fifth highest prison population per capita (behind El Salvador, Rwanda, Turkmenistan and Cuba), and you want to consider adding potentially another 600,000 (40% more) people to that population?

That would put us at the highest prison population in the world, and it would be not even close. That would be twenty per cent higher than some of the world's most despotic, dysfunctional countries.

And the same people who are not willing to fund socioeconomic initiatives, not willing to fund access to mental healthcare, are also not willing to fund improvements to American prisons which, while not the worst in the world, are certainly not even close to the pack when it comes to humane conditions, improving situation and circumstance, and reducing recidivism.

How would such a person get to leave prison if they were there because they were homeless? They leave prison and they're still homeless (see: already vastly overwhelmed transitional support structures, and a huge influx of additional demand and suffocatingly small desire to improve that situation).