(IFF) you are "renting" someone a necessity (THEN) they should receive something tangible in return for their money.
I live in Michigan, a roof over one's head is very tangible this time of year.
(IFF) you want to sell some space in your home (THEN) fractionalize your home and sell the fractions (like shares of stock in a corporation).
I purchased a four bedroom house for $94,500. If I did as you propose then let's say the value of each bedroom to be around $10,000-$12,000 (some value tied up in common areas such as the kitchen and living room). Not everyone has that type of cash laying around.
Of course it makes sense that "single family homes" would have different rules than an apartment complex or other commercial property, but I'm just trying to integrate your example.
The concept is the same. Let's say an apartment complex worth $2 million has 50 units being rented out. Fractionalized, each of those units are valued at about $40,000. Again not everyone has that kind of cash to spare.
Perhaps you could convert your home into a "private club" with a very exclusive membership list that stipulates dues are paid monthly?
This would essentially be renting. All this would do is avoid the stigma of the actual word "rent", which does not seem helpful.
Demand for housing would spike
Naked assertion.
while supply at best remains stable,
Naked assertion.
thus all else being equal property prices would increase.
Naked assertion.
I explained why this is the case from an economic perspective in more detail in post 112. Not a naked assertion, just naked facts.