In Investment Banking it's a well known rule that "prices are made on the margin" or in other words that the bulk of the assets on an asset type are rarelly traded and thus do not participate in the making of prices: it's it only a small percentage of the assets of that type that get traded and is responsible for setting of prices for all the assets of that class.

This is more true for lower liquidity markets like housing (were most units spend decades without being traded) than in Stocksmarkets, so yeah, you only need to push a small percentage of the total housing market (a fraction of the small fraction that gets traded) one way or another to change the price of all houses.

Also if the will was there (which is not, IMHO, as the main secondary source of income of almost all top elected politicians in Portugal is "realestate investment", even at the local level in the large cities) and now that the highest court has ruled that housing units in appartment buildings cannot get licenses as AirBnB business without the unanimous approval of all owners of all units in that building, a mere 2 measures would correct the problem:

• A requirement of being a Resident in Portugal to be able to buy residential realestate in Portugal, like various countries have.
• A massive program of building Public Housing.

The first would massivelly reduce Demand from foreign investors (whilst being within EU rules, as there is no discrimination between national and EU citizens as the rule applies the same to all), the second would increase supply and, as pointed above, as prices are made on the margin you don't need to add that much of a fraction of the whole market in newbuilds to significantly change the price.