No there wouldn’t really be. Luckily there are loads of restrictions, not least the restriction on building and development.
Ha Ha Ha Ha. Bollocks. The total inconsistency is laughable, the PDNPA is pretty toothless in anything other than making it hard for people who live here to do anything as they have some notional idea of preserving the landscape in some mythical period of time that never existed. But because the major landowners, mineral extractors and county council have all the power, they exercise what little power they do posses to mess with ordinary people just trying to have a life. (Also amazing how many people in positions of influence over the Peak live elsewhere)
Edit: Oh and if they can’t stop 4x4s driving on restricted byways, trying to stop residents getting in and out without paying should be something to behold. So no, not a good idea.