I mean, sure. At the end of the day all land owners, and I speak as one, exist at the end of a chain that began with theft and likely violence. The surface of the earth is by nature no less a resource that should be common to all man as the atmosphere and the oceans. Neither the landlord with more than he can live on nor the renter with not enough to live on can exist without someone at some point having taken more than their fair share by guile or force of arms.
Owning as the only housing model doesn’t make sense. There’s plenty of reasons someone might prefer to rent instead, most of them having to do with not being in a position to put down roots. Which necessitates some kind of landlord.
Money. The shares you are talking about already exist, and they're called "money". Of course, the relative value of shares wrt. the house will fluctuate over time and you'd have to account for this when transferring between houses, except this is calculated for you by the market when you just use money.
The sin isn't heritable but land, like artifacts in the British Museum, doesn't stop being stolen because we've had it a long time or traded it amongst ourselves. I'm not advocating anything radical; I'm just saying it's reasonable to be a little uncomfortable about it sometimes.
If you grow carrots, you would prefer to keep the overall supply of carrots low so that your carrots will fetch the highest price. But what you are actually doing is increasing the supply of carrots. So incentives and results are two different things and we shouldn't conflate the two.
I assume by "incentives", you mean that they'd manipulate the law to limit other suppliers. I'm sure that happens, but as a landlord you don't have to do that. And being a landlord (who isn't manipulating the law) doesn't make the problem any worse.
Criticism should be directed at the real problems. Those are a mix of law and culture and just inertia.
I don't know what you mean "rarely", because clearly a lot of housing is built and intended as rental property.
Regardless, the small landlord who buys a single family house and rents it out still puts a new house into the rental market, making it more affordable than it previously was on the purchase market. Along the way a landlord typically makes improvements and pays for maintenance, which improves the supply.
If you don't like laws then complain about the laws. The act of renting a house to someone else is not the problem.
It's pretty obvious that the cause of unaffordable housing is elsewhere. But being the one to actually collect rent is a kind of guilt-by-association.