I wonder what the Grouse population would be like if the Grouse Moors were allowed to "run wild"?

Managed Moors burn the Heather to promote new growth but it's not burned willy-nilly. You can burn against the wind for a deep burn or burn with the wind for a light burn. A light burn done regularly promotes all growth, not just the Heather. The whole Moor isn't burned in one go, one season, it's done a bit at a time so there's a mixture of growth of all species on the Moor. Then there's the feed etc left for the Grouse which has medication in it to combat diseases.

The Grouse shooting season is short and the Grouse are not shot to annhilation.

Both Grouse shooting and Pheasant shooting attract criticism from the jealous factions and what's not realised is that without estates in the past managing woodlands for such shooting, there'd be very few woodlands left today.