allio:
I'm sorry, I just don't follow your reasoning. If overnight the government passed a rule that said nobody can own more than one house, you'd suddenly have a huge number of houses for sale and a huge number of former tenants who now needed a place to live. The logical assumption is that the majority of these former tenants would then purchase one of the hundreds of thousands of now-available houses, and probably be very happy about it. So where exactly does the shortage come from? Do you really think there are going to be ex-renters choosing to live on the streets when they could just take their old rent money and pay a mortgage on their own home with it?
There would likely be a one-time price adjustment (market crash on the scale never seen before) as basically renters would be virtually gifted houses from the landlords.
High income earners/ entrepreneurs and the wealthy who would find such a communist style property rights grab objectionable and leave the country. The very type of people who innovate and create employment.
Then, as the population increases there will be no houses to rent. People will either be in the streets or living with family and saving for deposits (or on the streets in many cases).
Those with money will not want to build, as who knows what rules may be taken in future to grab their house.
And, successful farmers may no longer be able expand their businesses -- due to the housing rule they will be unable to house their managers/workers. This will lower productivity over the long term as successful farming models are unable to propagate.
Holiday towns may be turned into ghost towns, as houses become derelict and occupied by squatters.
It could be a very bleak future indeed.
Maybe I exaggerate some of the effects, but equally maybe I miss many of the unintended consequences too.