Measuring by occupancy rate isn't accounting for landlords withholding units from the market in the expectation that they'll find a tenant/buyer willing to pay more for them later, which is an allocation of supply the same as if someone was living there, and is caused by overall supply constraints creating the expectation of continued high rents.

It also fails on the other end because there are many alternatives to local housing other than homelessness, like selecting less local housing with an unreasonably long commute or living in units designed for fewer occupants in violation of the fire code. You essentially have unaccounted for over-occupancy. People having more money doesn't solve any of those problems without more housing for the money to buy, and interferes with solving homelessness as well because higher wages in general could cause people in those situations to move to existing unoccupied units before the existing homeless do.