I don't know; are you imagining a world where the people who believe the Washington Post would purposefully fabricate photos will be convinced by running a signature check on those photos?
Also bear in mind that Photoshop does exist today, and even without AI it would be well within the budget of the Washington Post to do edits to photographs that would be good enough to convince most non-experts. I don't run into many people saying their photos are doctored, but the conspiracy theories around photos today don't seem to be swayed by saying, "experts say it's not doctored."
I think if a chain of trust requires ordinary people to check signatures, it's probably not going to matter very much? I've seen people comparing this to HTTPS; people don't check HTTPS certificates either. There's a reason why PGP and signed messages haven't taken off. And the biggest criticism of Matrix that I see today when I introduce new users is that identity verification is too hard and they don't care about it. And these are the reasonable people.
I'm trying to imagine talking to someone who believes the mainstream media is lying about everything and telling them that, "no, it's OK, Google the tech company that you hate and that you think is trying to swing the election checked some math from its hardware and it says the photo is real." I don't think that's going to persuade those people of anything.