I'm curious why no one's tried a modern spin on housing co-ops. The big advantage of owning comes from locking your housing costs against inflation/future price increases, as one is naturally short housing. Why can't I buy into a general fund with similar benefits?

e.g. Write a contract such that equity is accrued over time, while I pay dividends on the "financed" portion of the home. This would also provide a hedge for home owners against their home price going down as the fund's assets would be spread across multiple markets.

As an individual I'd net out to the same investment position as if I sold the equity portion of my home to a REIT, then re-invested the money into the same REIT.