Because most of it would be over-run with bracken and other scrub vegetation. No-one is going to protect the moors unless they have a vested interest in doing so, I'm afraid. That'd be landowners and shooty types, as far as the moors are concerned.
I think Ilkley moor was in danger of being covered by bracken once Bradford Council banned shooting. Now they've allowed it again, people have a reason to maintain the moorland environment, and so are doing.
I'm not judging wether it's a bad or good thing, just pointing out that without vested interests protecting the moorland environment, it would probably disappear if left to it's own 'natural' devices.
Like the old aristocracy used to protect the forests for hunting, shipbuilding timber, etc.