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.