Also changing culture to discourage people from aggregating in hustle and bustle anthills.

That's a recipe for urban/suburban sprawl and an absolute disaster for the environment.

Even low density housing through basic human presence distorts natural environments.

It's basically like this in terms of environmental impact:

No humans >>>>>>>>>>> a few humans >>> many humans >> enormous amounts of humans.

Reversing the entire Industrial Revolution seems harder than just building more houses.

Cities are far more efficient than having everyone smeared across vast swaths of suburbia. And changing culture in a targeted way is not exactly an easy thing to do.

I don't think that's possible (other than indirectly such as by improving high speed rail so people can benefit from cities without living there). By their nature cities provide greater access to desirable amenities such as art, culture, museums, and niche hobbies.

Art, culture, museums, and niche hobbies are only desirable if the culture (other meaning) deems them desirable.

My dude, people have been making art for at least tens of thousands of years. I don't think people are about to stop now.

Has there ever been a culture that didn't value entertainment or art?

Sure. You can pass a law that only New Yorkers are allowed to live in New York.

Is it passed on by birth right?

I guess that’s the city of liberty for you then.

I was more thinking on a national scale.

How does that make it better?

I think there are valid reasons to want to control immigration, supply of housing isn’t one of them.

You don't think that immigrants need a place to live? The more demand you have for a thing, the higher the price goes.

Big that’s easy to solve by building more.

If it were that easy, it would already have been done, no?

Just because something is easy doesn't mean the people in power have an incentive to do it. Or don't have an incentive not to do it.

People who have houses don't want others to have houses because that increases the value of the houses they own.

Then they make up stories about "neighbourhood character" and how it's gentrification that is driving up the prices.

It took me a while to get this, but it's "not wanting others to have houses" that increases the value of the houses they own.

There is also the "please don't concrete over every last piece of green space".

New houses aren't the solution to droves and droves of empty ones. There are plenty of existing homes that should be available.

Or you could leave.

Is there any actual numerical evidence that international immigration is on the same scale as intra-national migration as a source of housing demand?

Who then will build new houses?