We are building, but building takes time, and all the houses and apartments are bought by 'investors' that then use them for airbnb... This is even more true in places like portugal (and many others), where realestate prices are so high compared to normal peoples income (due to speculative and airbnb investments), that normal people cannot afford them anymore, and only people with a lot of money or other realestate (for mortgages) can buy them, and the best way to earn back investments is again, airbnb.

So, you need to both build new stuff and ban airbnb for any chance that normal people with normal incomes will ever be able to afford to buy anything decent to live in. Also somehow stop buying realestate for investments. Also fix zoning laws in many places. Also...

Housing doesn't follow the simplistic supply/demand model. What happens in a lot of places here in Europe during the past 10+ years of low interest rates: developers + investors buy land and buildings to develop them, either chopping up older larger apartments into smaller units or building new housing but they don't sell all of them at once after developing. They hold onto units and drip-feed the market to keep prices high, the lost opportunity cost of selling earlier is offset by selling later at the inflated price.

I bring up low interest rates because getting a larger amount for a mortgage is cheaper, buyers will go to banks to check what's the largest mortgage they can get to fit into their budget to then go shopping for a house, so the prices are directly correlated to how much credit you're able to get, pushing prices upwards which the investors/developers can scoop up.

Now prices are extremely high, mortgages aren't so easy to get and we see prices going down (here in Sweden there's been a 10-20% fall), but they are still much, much higher than 10-15 years ago. It's pushed people like me, with a decent salary but no family wealth whatsoever to be basically priced out of the market. I'd need to save about 20-30% of my net salary every month for about 2-3 years to afford just the down payment for a small apartment on the outskirts of the city. I'm not able to do that while my parents depend on me and I still have rent to pay.

If it were that easy and simple, it'd have been done.

The places where AirBNB and their like are causing problems are not in the places where there's abundant land going, it's in the areas where there's significant tourist demand. This is in the cultural hubs.

People with capital are able to buy up the limited stock of housing and make a lot more money through short-stay, rather than long-term tenants.

This causes major flow-on effects.

Businesses which cater to long-term residents find their customers disappearing, and leave in favour of those catering to tourists/visitors.

The nature of the people in the area change: people in short-term stays are less likely to respect the local cultural-norms like not partying until 3am, or other behaviours.

The people who work in the local businesses, find it harder to do so - instead having to commute from longer distances because they now can't afford the rents/property prices locally.

Knocking down a few apartment blocks and putting in more high-density accommodation won't solve it.

You cannot build new houses in Venice, or Amsterdam center. That's where tourists want to go, not in those new houses in the peripheries where you would forcibly relocate your citizens with the proposed housing projects.