Not American.

If it's rural why would you walk on roads? Aren't (whether human or animal) paths enough?

Rural America is a) not nice to trespassers(and you're bound to walk on private land if you're off the main streets) and b) is even more car dependent than urban areas, so human or animal paths usually don't exist.

If I'm not mistaking there need to be a sign or a fence plus intent, otherwise it's not trespassing from legal point of view.

Sure, but you'll run into rural people that will just chase you off with a shotgun instead of calling their lawyer and once you've had that experience once, its enough. Ahmaud Arbery is a tragedy that paints this picture pretty well.

There are so few paths there! Germany has layers of paths wherever you look, but they're suspiciously absent from Canadian cities.

In many places, you'd be walking directly on a road with fast vehicles that don't expect pedestrians there. Look up "stroads" and you'll understand why it sucks to walk in North America.

There is literally no other path you are legally permitted to use in many places.