However, there is one critical component that must be present for that to work. 

But they add a component of refinance to get cash out of their rehabs to reinvest in new property. 

Being a general contractor and an experienced investor I see stuff from multiple angles and the key component of what you said was he is selling this property in the winter and that's exactly for a reason I've seen this happen many many times.

This appears to be a huge CapEx cost on top of the other major mechanical components of the house.

Those are two very key components. 

Multifamily falls out of style - Cap Rates inflate.Yes, there are baseline economic relationships, but there is a psychological component.

If this is no interest component, you need to impute interest. 

I'm looking at this, forstarters, from a tax point of view: if you have a mortgage then you can deduct "that" (= the non-principal components) from your rental income.

Maybe create a non-profit with the express goal of raising funds to bring the properties back... with some sort of low income housing component.

Bottom line though for a buy and hold investor Property tax's are an important component and all things being equal if your in non appreciating states. .Like Texas basically has been for ever and a day ( except Austin ) and the little bit of run up they have had..