In somewhere like the UK the "authority" can be the large land owner/aristocrat. And individuals own relatively little land. It is the kind of thing that Americans escaped from! In that context public access is a defence of individual rights. And often rights will have existed for hundreds or even thousands of years. Public access is a defence of that.

But I think the different culture of America is a really good practical reason against improving access for the public. Guns alone would make it risky.