I've deliberately avoided this thread, and I think my opinions might surprise quite a few people on here. I love walking and I don't drive. I use public transport to get to loads of places. But this doesn't make me anti-motor vehicles.
I don't see outdoor access by motorvehicles (motorbikes or 4x4s) as being incompatibe with what we do at all. I spent my teenage years sitting in a trials sidecar most weekends, getting out into Shropshire and Mid-Wales. My interest in the countryside and in that part of the world stems directly from those trips. As a member of the Byways and Bridleways Trust and LARA, my Dad spent the last 20 years of his life campaigning to keep rights of way open, for walkers, horseriders and also byways for vehicles. He very much believed in the maxim "once a highway, always a highway". He also believed that access should be for everyone.
As with most things, in my opinion the problems stem from (1) a minority of idiots and (2) overuse. Ths is true with walkers in the mountains, climbers on rock and with this subject too. In much of my walking expericence, horses' hooves have caused worse damage to paths than motor vehicles. Tractors, which use country green lanes because the farmer either owns the land himself or has a private right of way (as opposed to any kind of public right) are also very damaging. The damage caused by motorcycles and 4x4s used on public rights of way by the public (not the landowners) is very small in comparison.
In terms of pollution, etc, far bigger strides could be made if parents took their kids to local schools without using cars, if people walked to the shops rather than driving half a mile. These would be far more beneficial to the environment than stopping a fairly small number of off-road users from getting out into the countryside.
Regarding motor users in the Peaks specifically, it's a bit old now, but see the headline story here:
