> In Prague, they started removing rent controls several years ago, and we have seen highest increase in property values in maybe three decades.
Property values are not the same as rents or general housing costs. As soon as you make construction more profitable, it makes the land worth more -- property values go up. But then the construction happens and housing costs, i.e. price per unit, go down as a result of more units.
Before you had two housing units on $500K in land going for $1000/month. After the land is worth $2M but it has 20 housing units going for $750 -- and the landlord is making more revenue, because 20x$750 is more than 2x$1000, enough to offset the higher property cost.
> Also, if I owned some property, I am not sure I would want to invest in building new one and have to decrease rent rather than enjoy the fact that the rent is high.
Rent doesn't materially decrease as a result of one person building one building, it's a result of many new buildings across the city. So your choice isn't between the existing two units at $1000 and twenty new ones at $750 (though even that itself is still profitable), because if you do nothing the existing units will still fall to $750 each as a result of what other people do once they're allowed to do it.
> More important is probably lack of actual housing construction financed by government.
Actual construction subsidies might help when you have a massive shortage and you want it correct it quickly, but in general it isn't necessary -- when rents are high and construction is permitted, it happens.