Alice and Bob don't help or hinder your argument in any way. It just seems like a non sequitur.
Selection of choice to rent vs buy typically isn't driven by net wealth change considerations; rather, it's an investment in an area, because the transaction costs of house purchases are much higher than changing rental leases, and thus you need to stay in a bought house longer to spread the costs. In particular, houses bought for living (rather than rental) are more often selected for life-changing events, like starting a family, or downsizing when children have left the family home.
Further, your bald assertion that unrealized rental income will be greater than rent expense otherwise incurred - if I read this right, it means you think people will buy a more expensive property than they would rent - I think is wholly unjustified. I think you've got it exactly backward, and that's certainly the case in my rental vs purchasing history: I've always rented places that I couldn't afford to buy.
When I was younger, I valued being closer to the heart of the city (London in my case). That meant denser living, apartments, etc. When I chose to buy, I couldn't afford to buy the places I'd been renting, but also my values had changed: I wanted somewhere with more space, not least because I had more stuff (like motorcycles, which meant a garage; and an office distinct from the living room; etc.)