It could, but once sold it might never again be accessible to the public.
I prefer the Scandinavian approach: Non built up land can be freely accessed by anyone regardless of owner in most cases, and the coast is by default protected against people building down to it in Norway at least. Dispensations do get given, but if you block access without applying for planning consent, it will be struck down.
The basis is simple: Restricting access to a scarce resource like the land is equivalent to taking away or liberty. This is a right we've had since time immemorial - in Sweden it's a constitutional right. In Norway it was not codified into law until the 60's as it used to be seen as so self-evident that it wasn't necessary.