I love veterans as much as anybody, and this might be politically incorrect from both the left and right, but I don't support giving out houses to homeless vets for the same reason I don't support it for other homeless people. It isn't what they need. And I might get ripped for saying so, but veterans get a ton of benefits to help them become educated, find housing, get healthcare, and find work. Businesses generally like hiring veterans, and of course most government jobs have a veterans preference. They deserve it all, but those who become homeless don't need to be given free houses. They don't lack resources or need a handout. They need treatment for whatever is keeping them from taking advantage of the myriad of benefits for which they are eligible.
As a veteran I agree with most of what you said. My brother is a veteran and came out way more f*ucked up than me both physically and mentally. He hasn't worked since he retired about 12 years ago but has full disability, retirement and medical benefits. He also saved and invested wisely while enlisted and is set. Bought 200+ acres in the mountains of Tennessee, built a cabin and is living as good as he can. He's about a crazy as can be and is living well mostly off the grid. His wife is now getting her second degree for free because of him. She's doing it just because she can and its free. That annoys the **** out of me because the benefits shouldn't be eligible for things like that. Most vets are fine. We (my company) build houses for vets who come back paralyzed or physically disabled and can't work. I draw the line at the medical conditions both mental and physical. If you serve and come back screwed up then those conditions need to be treated. Level of disability determines benefits. Just being a homeless vet doesn't mean you deserve a house or more benefits than the average person. Life choices matter even while serving.