1) "Multiple" here is wrong. What is the time when you own two houses? Well, when you're moving! You buy one, then you sell the other. During that time, you own two houses. That's multiple. Study the hermit crab.
2) Your three percent cap means that property renovation, repair, expansion, and so on is completely doomed. Why didn't you think of that?
This stuff is complex. It requires some careful, thoughtful approaches.
You want to sell your house and it has 200k valuation? A flipper will give you 200k so you can buy another house, renovate without owning it and then at sell for say 250k and the benefit to the seller would be splitting the 50k with the renovator with whatever percentage they agree on. The key difference being the flipper now has an incentive to sell soon instead of wait years until the house costs say 500k because the original seller wants his cut soon so they can move on.
Flippers will not be doomed but flipping will be less profitable than it is now unless you do it at scale of course.
For your first point is it not obvious I meant at the time you place the house on market you if you owned multiple houses?
Is this comment allowed on the internet?
Not enough. That's how you get a voter base which pushes for plans which make properties more expensive, deprioritizes building and depending on other variables, causes population growth while telling the next generations to just deal with the smaller piece of the pie they have to share with a bigger population than before. That mentality effectively means you're dependent on home owners as a whole to care enough about others to prioritize their needs. Historically, this hasn't been true for almost a century in the majority of the developed world.
That's also why this problem is so difficult to tackle. We don't have a critical mass of individuals democratically yet, nor a critical mass willing to cause enough damage to make voters care. And the majority of politicians do not care enough about the long term consequences (or alternatively, realize caring about the long term consequences won't win them votes).
This makes it more profitable to sit and collect rent than to sell. Property will never change hands. I hope the current owner knows how to build.
With the exception of employee housing, any non-individual entity including agents of corporations should not be allowed to purchase even one residential property.
With the exception of diplomats, foreign citizens should not be allowed to purchase more than one property.
These laws should be applied in any developed country.
This is one of the reasons they wanted corporations to have rights as a person, because in regular reasoning a corporation owning houses, making speeches and donating to parties makes no sense as their activity and existence is entirely in the sphere of privileges not rights.