(Tax incentives skew these incentives towards ownership.)
Most of the gains from active REI don't come from RE appreciation (which generally tracks the inflation rate nationally). The growth from REI comes from using a TON of leverage to purchase the assets (ie a mortgage) then getting someone else to build your equity for you (the renter).
Additionally real estate investors pursue extremely favorable deals, generally where the seller is motivated to use their built up equity to sell at a significant discount to what the remaining cost of their mortgage is. These distressed sellers are usually going through a divorce or potential bankruptcy (where getting a small amount of their equity value back is preferable to losing everything and destroying their credit via bankruptcy).
As you alluded to, this of course relates to real estate as a business. Not to standard home ownership (where you buy a property because you want it as a home, not because it is a good business investment).
It seems like it'd be a better idea to continue paying rent and just buy some shares in an REIT with the difference in cost with rent and rent+shares. And let's be clear: You would pay higher rent in your scheme, so said difference is nonzero.