This is a concern and ought to be a concern to the tourism bodies. Plenty of us come to Dartmoor exclusively for caching or letterboxing- read the logs from cachers from away and you will see plenty of comments like”the rest of the series will have to wait until my next visit”.
In some ways Dartmoor ranges are unique. I cannot imagine trying to put a cache on the Sennybridge military range just next door to me. Indeed in areas such as Sennybridge or Castlemartin in Pembrokeshire, this is already policy. There is no public access at all.
As said, there is a considerable logistic nightmare to enforce this. About the only bit of the high Brecon Beacons that it has been possible to place a cache on is the eastern half of the Penyfan massif which is owned by the Honourable Artillery Company. They are a territorial unit but own property themselves. Is that military land? There is only low-intensity training there- basically yomping over it. And HAC and their agents have proved themselves to be pro activities such as geocaching by granting permission.