if you manage moorland with the intent of increasing biodiversity you can and this produces greater biodiversity than managing it soley for shooting
But, and its a big, huge capital BUT – in the process of doing so you decrease its value for internationally endangered characteristic moorland non game species
golden plover, curlew, and lapwing populations are lower on moors managed in the way you propose – all of these species have recently declined in geographic range in Britain!
This is a prime example of the Red Squirrel dilemma and you still have not tackled it!