The blanket ban is there for a reason and anyone who has experience of the fires that used to happen on very regular basis will understand why.
The problem is that unless you are an authority on the flora and fauna of this country and specifically the region you're camping in (in this case Dartmoor) how are you going to know if you are destroying a minute orchid or unearthing a grub / pupae that will then dry out and die that could possibly be rare or endangered.
I support the leave no trace principal, I believe in it very much so, but our problem is that's just me and a select handful of others that abide by it.
I have as has already been mentioned, been on the moor walking the trails through areas of amazing beauty just to come across an obvious fire pit that has either been left to burn out or has had a token effort to dissipate the resulting devastation all over. The beer bottles / cans, the rubbish that people cannot be bothered to carry out with them.
One such glade was literally on a place on Dartmoor that has got a rare species of orchid and grubs for a specific insect and the area had been ruined.
There are no rules to stop people using camping stoves / barbecues on the open moor or even in some of woodland near the rivers and streams, so why not use them. Take away what you bring in (your rubbish), leave the place as it should be, but don't start fires unless you have the authority to do so (some land owners will allow fires on their land if you ask them first and clean up after yourself).
There are campsites on the moor that will allow open fires, use them if you want one.
The other option would be an authorised group or body that will teach people the correct way of doing things using specific locations approved by the parks authority. Then if you wish to go onto Dartmoor and start a fire you have a guide that will both show you the places where you can and how best to do this whilst leaving no trace. This can be tied in with the authority and monies paid in can then be used by the authority to help manage the national park.
It will never happen in all probability, but it is a nice idea