The sooner we collectively decide that housing shouldn't be a market, the better. We all need it, and we should figure out mechanisms to make it available to all. Practically that means paying to build and maintain housing stocks, changing tax incentives so developers are incentivized to build more housing and less luxury housing, charging a premium for unused land in desirable areas (parking lots don't house people)…
Yes, we can and should regulate markets, and we probably all agree that the purpose of the housing is for people to have a roof over their head, as opposed to use housing as an (speculative) investment market. This can easily be regulated via taxes (on ownership and transactions), but it comes with a caveat: if something is over-regulated to benefit the user, then there is less incentive for investor/landlord to build housing, which makes housing scarcer and drives prices up.