Comment: The agreement is to be VOLUNTARY

Ideally the governments only involvement should be as a negotiator / go between / facilitator / publicist / encourager of more schemes or greater numbers.

The agreement should be between a bank and a Vets organisation.
E.G an agreement in each of the 50 states between a specific bank(s) and a vets charity/support org.
There may be more than one agreement in each state.

The banks would agree to house X number of homeless vets in their vacant properties.
If a property was sold or the bank wanted to re-take vacant possession the Vets would move to another of the banks (nearby) vacant properties.
If a vet abused the scheme or damaged a property, they would be issued with a warning and ultimately kicked out of the scheme.
Some arrangement could be made for property damage in the scheme so the banks were not put at too great a risk. Details to be negotiated, but it is basically an insurance scheme - cover for a large number of relatively small risks.

The government would publicise such agreements by e.g. holding a press conference that a certain bank was supporting Veterans in a certain state.

The banks would get the opportunity of running ads stating that they were supporting the troops (vets).
A great business opportunity for banks which currently have a very poor reputation with the general public.

Hopefully the banks would give free accommodation, in return for the positive publicity and branding.
At worst vet charities would pay a nominal rent for each homeless vet housed.

Vets would share each house - 1 vet per bedroom.
Group therapy without a psychiatrist (much better than with a psychiatrist).

Some banks would not want to do it.
Some would.

The schemes could start off small - say 100 vets as a pilot scheme.
If successful it could be expanded to a thousand or more vets in each state.
The government would arrange a press conference for the good news of expanded collaboration between said bank and vet orgs/charities.

Do you not think such a scheme might be a runner?
Do you not think that such a scheme might be expanded to cover tens of thousands of currently homeless vets at a nett (small) benefit to taxpayers?

It does not cost much to write a glowing report or hold a press conference or hold a 1 hour meeting(s) as moderator between several banks and vets organizations to facilitate such schemes.

win/win/win/win.
Vets, taxpayers, government & banks.

The government would win for it's increased reputation as a practical facilitator of solving real world problems with real world solutions (without costing $$$).

The taxpayers would win for a small saving and/or a feeling of general satisfaction for helping vets that found themselves on hard times.

The vets and bank wins are self explanatory.

The above could be termed common sense and thinking things through.
I am a great advocate of common sense and thinking things through to achieve practical solutions to real world problems.
I am not into idealism or dogma.