I find this discussion quite interesting. From a German perspective there's almost infinite amount of space in the US for hiking, compared to Germany. You find a lot of great trail in Germany, but if you go to Neuschwanstein (AKA the disney castle) you will find huge American and Chinese tour groups. But most other trails are perfectly fine. I can't imagine with the wide selection in the
US to have any problem if you're not going to one of the top 5 search results.
You get a lot of tourists in the US at the top parks as well. It's gotten so bad, many national parks are requiring reservations to get in, something they've never done before.