If u look at the NZ example DoC (dept of conservation) owns massive massive amounts of land and builds and maintains huts (althou some are pretty rough).
Foirdland alone could be a similar size to wales in 1 continuous inaccessible block.
In most of NZ u can pretty much please urself wot u shoot, no real seasons and very little retriction on DoC land (apart from during the roar on very busy bits of land where its a free draw for beats)
But the size of some of the woods/land are gigantic, we flew in to a hut that was 4 days walk from the nearest dirt track and it was just on the edge when u looked at the map, the big difference is that there is not the same demand on forestry by other recreational users, dog walkers, bikers, hikers, runners.
Most FC woods are open access and in many cases it's actively encouraged.
I do agree with exactly wot sir lamp a lot said, sometimes it's a good thing that not everyone can just get out shooting.
I can't see any different fair way of doing it, there's simply too many stalkers after too little land that is already busy with people esp nearer the big cities.