If the problem is exacerbated by active policy or indirect action/non-action, then as a collection of people/states it is the burden of every state to shoulder it. And the federal government is just that, the collective power of all states combined.
So, lets imagine that the problem is being caused by other states sending their homeless over. Well, in the US you can't stop that, at least by direct migration, you might be able to stop particular organizations like city governments from doing so. But in a general sense there is freedom of movement.
The problem comes with that, the better you're at solving homelessness the more people will get sent there, and even more homeless will want to come there even if they are not sent. Suddenly Texas, for example would see California spending billions on the problem... Texas would have no motivation of spending billions to solve the problem themselves, in fact in terms of getting rid of the appearance of a homeless problem it would be more beneficial for them to be draconian on homelessness. This would push individuals to migrate to the promise land of California.
California would see is homeless costs increase dramatically and would be incentivized to stop (increasing?) funding on the problem themselves. Moloch wins. More people suffer. Yay humanity.
If it is not caused by other states, that would indicate that the problem is something happening in California, and maybe a state level solution is best.
You have to start the solution in the right place to have any hope of addressing the root cause.
Edit: I dug up some data:
https://www.nytimes.com/2019/11/06/us/homeless-population.ht...
> As the data shows us, most of the homeless people you pass on the streets every day are in fact Californians.
> “This is a local crisis and a homegrown problem,” said Peter Lynn, the executive director of the Los Angeles Homeless Services Authority, the agency that conducts the largest homeless census count in the country.
> L.A.H.S.A.’s 2019 homeless count found that 64 percent of the 58,936 Los Angeles County residents experiencing homelessness had lived in the city for more than 10 years.
CA considers you a resident for tax purposes if you live in the state for a year but in homeless studies they consider you a resident if you live here for more than 10 years. Really shows the bias.