Your argument against rent control is a good one, but it has a fatal flaw. When you say
the problem is that, in a stable market, prices properly reflect the position of supply versus demand
you're correct. However, accomodation is not a completely open market, and thus purely market forces do not suffice to stabilise it. Accommodation is a limited resource, and usually people have little choice where they live once they take a given job.
The situation in Dublin in the '90s is a good example. At the start of the decades, rents were cheap by European standards. Even in 1996, when I moved to Dublin, I was paying £35 ($50) a week for a bedsit, which became £40 ($57) a week in a house-share soon after.
Then the job market exploded. The population of Dublin and its greater metropolitan area went up from under a million in 1991 to 1.4 million (including satellite towns) in 2002. My rent went from £35 a week to £450 ($600) a month when I moved to a 40 m2 (400 sq ft) apartment in 99, and from there to £750 (over $1000) a month when we moved to a slightly bigger apartment - 55m2 (550 sq ft) in 2000. That's an inflation rate of 300% or 400%, which was caused by a mix of market factors and geographical factors.
- More meople were arriving in Dublin than there were places to accommodate them
- Dublin's design (and planning laws) meant that it was hard to accommodate everyone in the town, leading to some urban sprawl
- Houses were coming on the market 6 to 9 months after they were needed, leading to a tulip war over new houses
- People needed accommodation, so to get what little there was, took bigger loans at the bank
- The banks, seeing the market explode, were happy to give people more money than they could afford to pay back easily.
- More and more people were buying property as an investment, raising rents to pay back mortgages
- Most of the people migrating to Dublin were in the 20-30 age bracket, and most of them could not afford to buy at market prices
The classic laws of supply and demand make assumptions about buyers and sellers (such as, if a buyer is charging too much for a good, the seller can decide not to buy it) - the situation in the real world where a good is both a necessity and in limited supply mean that controlling the market is sometimes a good idea.
Just to clarify what I mean by rent control: when you agree to let a property at a specific rent, you are limited in the frequency of rent increases, and in their amount, by the law. Typical restrictions might be "no increase for 2 years, then no more than 3% per year". So if you rent an apartment in 2000 at $500 a month, then you know that your rent will not be any more than $515 a month in 2002.
In situations where rent control is in place (such as France), market pressures can still force rises in property prices and rental prices, while protecting existing tenants from landlords. Not that that's a bad thing, but it means you can't arbitrarily raise the rent to get in a "better" tenant, putting some poor 70 year old woman who worked all her life embroidering tablecloths out on the street.