Yeah this was my immediate impression as well. The assertion that homing every homeless person is the same as putting them up in unique per-person accommodation that ends up costing 65 billion is absurd.
Also, how do you solve homelessness? Giving every homeless person a subsidised house isn't going to work out if that person can't afford it (especially when the subsidies run out), because they're also unemployed, or because they have a drinking problem which means they trash the house or spend all their income on alcohol and can't afford rent. For some people, temporary free housing, rehab, and help with finding employment could be a cheap and effective way to get them back on track and able to afford a place with their own income after a few months.
That's the problem: there are many completely different situations that lead someone to become homeless, and the solutions must be tailored to the specific case you are targeting. (it's a variant of the Anna Karenina principle: “All happy families are alike; each unhappy family is unhappy in its own way.”)
And you also need to take into account the role of homelessness as a coercive force in modern societies: it the treat that keeps worker behave at work, prevent unhappy women from leaving their husband, and make sure tenants pay their rent to their landlord and make sure people repay their mortgage before any other expense. Remove it suddenly and then you'll probably end up needing way more housing than what you planned for previously homeless people. And it would absolutely tank the real estate market.
I'm convinced that all of the above would be a good thing for society, but the shock would be absolutely gigantic. It's not just about investing a few billions of dollar, the cost of the housing per se would be negligible in the earthquake that it would cause.
Came here to say this. It takes political will, but money is certainly not the issue. It's just like with healthcare, free healthcare for all costs much less per person than privatized healthcare like they have in the USA. It's just a matter of designing the system properly so the money doesn't get siphoned off by parasite investors.