With regard to the Stanage Causeway video, TBH, I used to go to Stanage climbing on a regular basis, and hardly ever saw or heard the motorised traffic that uses the Causeway. I tended to be more embarrassed about fellow climbers who thought that littering and endless high volume effing and jeffing was the order of the day.
If you'd have posted it as a heads-up camera from an MTB with the volume turned down, it would not have seemed particularly extraordinary. It was early morning, they weren't forcing pedestrians out of the way, or even going particularly fast.
On that track in those conditions, the only impact is the noise. For four minutes gate to gate. If I ruled the world (!) I would probably aim more to get quieter exhausts on these bikes.
So it's legal, and while it isn't ideal for other user groups, I don't see anything in this particular clip that's going to have me tearing my hair out. If you go to Stanage at the weekends seeking some kind of rural tranquility you'll probably be disappointed anyway. The air ambulance seems to turn up at some point most weekends...
Getting bikes and 4x4s off bridleways and particularly vulnerable BOATs (Like Foxup) would be my priority.