In the Alps, where there is the most dramatic scenario, in France, Switzerland, Italy, Austria, there aren't a lot of areas where you can just pick a spot and camp there.
You don't need a permit to stay in a hut/refuge, but you usually need a reservation, which is sorta the same thing, a limit to the number of overnight visitors. Effectively a permit.
There are very very very few places in the USA where you need a permit to just hike for the day. Places where they are required are either very vulnerable like "The Wave" in Utah or dangerous when overcrowded like Angels Landing in Zion.
If Sweden counts as Western Europe, we might as well add Finland to this list too.
Besides a few exceptions (military bases, the border zone, a few protected natural parks) you have an absolute right to camp anywhere as long as you don’t cause more than minor harm to the landowner.
Wonderful bike trail, has realistic information on where you can camp for each country.
In the Balkans people camp regularly on the side of the road on public lands. I have friends that did it in almost every country in the region on motorcycle tours, so they were camping quite close to roads.
In France you cannot do wild camping at all, bivouacking is merely tolerated. In some trails, you can only set up camp in designated spot.
If you go to the mountains actually, you will see tons of folks camping around all the time, nobody has any issue with it. The only exception are proper natural parks, but that's understandable.
I'm saying, the management of public land in the USA is DIFFERENT. Even different than Canada.