I actually cycled this route a few weeks ago, I can see why people are upset. There has been a large number of vehicles come through that have absolutely chewed up the ground, in places there are multiple pathways formed as one has become impassable.
Maintaining vehicle and cycling access, as well as marking out where the road actually is, is the best outcome in my view.
Yes, you cannot obstruct passage. Although I’m not sure if the road itself is considered private.