You seem to take the free market as a premise and from there deduce that it is a desirable construct. The point was that the nature of the free market has an undesirable effect on prices.
Quite a good comment. I had never considered that taking the free market as a premise might not be the correct decision.
On further reflection, I still think it is the correct decision.
If someone wants to rent a property more badly than anyone else wants to (i.e. they are willing to pay more) then why shouldn't they get it instead of the others? This will push prices up, but that's a natural effect of allocating scarce resources to whoever wants them most.
I think you have accidentally conflated "whoever wants them most" with whoever is willing and able to pay the most.
I am not sure how you would find out whether I want to live on the street where I grew up more than, for example, a billionaire Russian oligarch, but I think that even if I wanted it one thousand times more I would remain unable to afford it.
It may be that many other people gave the oligarch some money to show that they, in some exchange, had a total want for said oligarch to live there more than my want, but this is a different claim implying a very strong assumption about the addition and fungibility of wants, making them indistinguishable from money itself.
