Virtually every property borders public land of some kind (a public road right of way, typically). It might be interesting to minimally specify what it means to allow access in a way that doesn't allow virtually any path across one's land. You can't just require allowance from any other border directly to the nearest border of public land, for this reason (could be through the owner's house or garden). One way might be to require the specification of public traversal areas as part of the title. Or 100m around the edges of every property is traversable.
Specifying some minimum property size should cover most cases, as well as specifying land uses that are or are not covered by the requirement for public access.
If you own a large parcel of land but are actively farming it, I think disallowing public access is reasonable. If you own hundreds of acres of wilderness, I think public access to traverse the wild areas of your property is perfectly reasonable, even light camping with reasonable restrictions. Specific issues can be prosecuted individually, instead of a blanket ban on all public access.
