We need that freedom. I would also say that we also need education on how to use that freedom, how to not leave a mess behind, how to preserve those places for others.
It is. It requires an attitude that restrictive property rights takes liberty away from the public, and so must be balanced to minimize the restrictions they impose to be legitimate at all.
As a European I prefer the way we do things here, but I do envy the amount of publicly owned land in the US where citizens do have freedom to roam. e.g. National Parks, BLM & Forrest service land. We have less space, most land already owned by a private citizen since Feudal times.
Well, with freedom to roam it'd largely not matter if it's privately owned. With reasonable sensible rules you get the best of two worlds: You "only" need to take special measures for land that should be left unspoiled.
I used to walk through privately owned forests on the way to and from school and sometime go off walkthrough them with friends as a kid without once having to think about who the owner was, because it was irrelevant.