I don't disagree with any of that. But if you're framing the homelessness problem as a veteran homelessness problem then the applied solutions will likely leave non-veterans that still need help without. All homelessness is a problem. That is not the same as "all lives matter" because homelessness isn't primarily a problem that veterans face. They're estimated to make up 5 percent of the homeless population.
The government does have a particular responsibility to vets, and should be fixing that. But they have a responsibility to non-vets too. And the things that cause homelessness for veterans causes it for everyone else too. We can and should be helping veterans by addressing the root causes that effect everyone. But any solution that only results in helping vets (like supplying only veterans housing) when they could be helping everyone is unacceptable, particularly as plenty of people would consider the job done so long as the homeless that remain aren't vets.