I just pulled the cites/case notes on 91.11 and strangely they say nothing remotely like what you say it means. The latest FAA directives reference laser pointers and assaulting pilots. If the feds wanted to make it unlawful to disobey any crewmembers order or direction, they could've done so. It's a pretty easy thing to say, see I just did it. However, that is not what they said...I'm not saying it, the CFR is saying it.
Well, your hyperbole aside, it is a matter of priority. In that moment, the crewmember is king (or queen). If what is being done to the passenger is a breach of contract, on the plane is not the place for it.
You don't have to like it, now or in that moment. But, federal law says what it says.
In the air, the pilot makes the call. Well, not to deplane you, but to subdue you and divert.
What is a better approach? Allow the passengers to call the shots? Instead of an undercover TSA agent/air marshal, have a traveling ALJ on every flight?