Like you said, people could buy a stake in a property and get dividends from the profits derived from the property.
How would Bitcoin enable this better than fiat currency? The utility you're speaking of isn't possible only through bitcoin or blockchain technology.
Another angle is to get property title deeds to be moved onto blockchain. This would make transfer of property ownership an absolute breeze.
This is probably the best use of blockchain technology for real estate. And I'd go one step further than record of property ownership, and include all records of upkeep and maintenance over the house. This way the history of the home and it's care is infinitely more transparent, which will bring better and more honest valuations to the market.