They literally aren't, though. They are the airline's private property, and you've entered into a contract of carriage with them to temporarily have access to their property under the terms of the contract. To some extent these terms are circumscribed by law, but in the absence such law, you are bound by whatever terms you agreed to in the contract. If you don't agree not to film in the plane, you're free to not accept the contract.
> They literally aren't, though.
They literally are. They are common carriers, which is a legal concept with a lot of precedent. The UK term for this, ironically, is "public carrier" and while yes it's a privately owned it has distinctly public characteristics encoded in law that sharply distinguishes these spaces from genuinely private areas.
That's a distinction without a difference. There are enough structural constraints in launching airline alternatives that they might as well be, especially the national carriers. They are not too far from being a utility (and in a lot of places they are subject to enormous amount of public funding to stay solvent because it's a national security issue when you don't have a pool of pilots and airplanes).
It's one of those "too big and too important to fail" businesses. There can be the occasional M&A or bankruptcy but no structural industry collapse is allowed. It's as important as the car industry in some places, though the reasons differ.
Do you expect the masses to fly private jets or Cessnas to cross the globe? It's like saying electrical companies shouldn't be regulated too much in certain jurisdictions because the generators are privately owned rather than being publicly owned. People will laugh you out of the court of public opinion.
If you want to launch a public campaign to change the law and add "you can always surreptitiously record people on airlines" to the set of unenforceable contract terms, go ahead and attempt it. You'll deserve the furious blowback you get, though.