Don't you think that would just drive up the market price ? (by restricting supply i.e. making landlordship less desirable)
yeah, that didn't turn out so well for higher education and healthcare. so no to that.
housing markets are distorted in a thousand ways. a solution like that might be appealing for its simplicity, but what we need to do is the hard work of rationalizing a death by a thousand cuts. start by aggressively repealing every zoning/building regulation that's not tied to solid safety concerns (and not nebulous and nefarious ones). eventually you'd be in a position to repeal (in CA) both prop 13 and rent control (but not saying that'll happen), which are complementary distortions, but only when the market is functioning well enough not to need (for sociopolitical purposes, not economic ones) them.
Obviously not the best solution for the landlords, but, really, so what? Removing a class of parasites from the housing system would be a feature, not a bug.