Yeah, and what if they gave away houses out of the goodness of their hearts?

What-if games don't provide great insights in cases like these. Trust me, if it worked at these scales, you'd hear about it.

There are plenty of REITs operating in my city that have substantial detached residential holdings.

The EV on renting and holding substantially improves if the housing market takes off like a rocket. It might not work in your market, but that doesn't mean it doesn't exist.

Wild speculation and hypothesis doesn't mean it exists, either.

It's not a hypothesis. You don't need to believe it exists and it may be less common in your market. I know this is true firsthand as in the course of my work, I review the financial and legal side of these entities at times.