Then again - if people are moving in to already tight place, who is to blame? What are the probable ways of "tackling" it you suggest? Soviet-style "closing" of a place where the Party will decide if you are eligible to buy? This is how they prevented Moscow from overpopulating in the Soviet Union, resulting in doubling the population in the decade once barrier fell with the end of Communism.

If anything, it's a source of free money for the residents: sell your current house for millions and move out somewhere cheaper, maybe retiring early as a result.

If you don't want to people to move, analyse the reasons that push them to move and see what can be done about it. Real estate prices are just an indicator. It's stupid to "tackle" indicator rather than underlying reason.