I just want to note that even with these annoying carveouts, the US has far more federal land than other European countries. There's not really an equivalent to the vast national forests in the US west in Europe. Those countries are essentially 100% allocated and settled.
But also, the corner crossing thing is really dumb. Why did the federal government establish a checkerboard pattern? Either way, they should just eminent domain 20 feet off the corners and call it a day.
It basically worked, except in wooded areas where the value came from the timber rather than the land.
Is it really true that nobody in Germany is allowed to fence their property?
Oh, and you're not allowed to build any cabins either, even if you own that piece of forest.
However, I'm not certain that that's the case everywhere in Germany or only in some states.
There is property where you can build a proper house and live there (requirement is, that there is infrastructure, like water and electricity). Then there are gardens, where maybe a small cabin is allowed (but you may not officially live there). And then there is everything else, where you normally cannot build anything.