Maybe, but…presentism? Europe could do what the US has done and declared so much land federally protected that growth is stifled and property rises to a level that prevents the young from buying it. Although that’s a different topic…
That’s a problem but it has nothing to do with protected park land. Much of it was driven by racism: white people started leaving cities following civil rights era losses and sprawling out into adjacent suburbs, which were often forced to be low-density to exclude poorer people. That locks in a hefty climate footprint with all of that driving and larger low-efficiency houses.
The land that is federally protected is generally not exactly sites so as to make for prime housing. Most of it, by area, is in places like northern Alaska.