Are pilot YouTubers breaking any rules?
If the FAA considered making videos itself (i.e. separate from any unrelated rule violations within those videos) to be a problem, they would have put a stop to it long ago, either by explicit rulemaking or the catch-all "careless or reckless" when no other rule applies. They haven't, at least with respect to GA pilots--who are allowed to do all sorts or things that charter and airline pilots are not.

Several YouTubers I follow have said they mount the cameras and start recording before preflight, don't touch them again until after the plane is down and secured, and edit out the boring parts later that show this.  That seems to mitigate the physical safety issues.

The other issue is pilot distraction if they're talking to the camera, but I don't see that as any worse than talking to passengers, which is commonly accepted within reason, and is perhaps less of a risk since the camera doesn't talk back.