"can't easily be extracted" = "the number of people who can extract it is small but still non-zero"
And those people now have the power to put you in jail, by putting your camera's signature on illegal content.
You've also just made journalism 3 notches harder. Like documenting atrocities in, say, North Korea. Or for whistleblowers in your home steel mill run by a corporate slavedriver.
Oh. Also. Why are you choosing the camera side to put this on? Why not the AI side? Require watermarks and signatures for anything created in such a way…
…of course that has its own set of intractable problems.
Ideally, the keys would be per-manufacturer, like HDCP or (DVD-)CSS. Personally I don't think I'd love the idea of any kind of attestation like this, but if TPTB did implement it, I'd prefer a key per-manufacturer rather than each unit having its own unique signing key. We do have precedent, in the form of printer tracking dots, which were kept 'secret' from the public for 20 years. [0]
0: https://en.wikipedia.org/wiki/Printer_tracking_dots