Why don't social media and the web in general implement asymmetric key signing to always be able to verify the source of a content, thus eliminating the risk of deep fakes and fake news?

I don't understand how this will help deep fake and fake news.

Like, if this post was signed, you would know for sure it was indeed posted by @lily33@lemm.ee, and not by a malicious lemm.ee admin or hacker*. But the signature can't really guarantee the truthfulness of the content. I could make a signed post that claiming that the Earth is flat - or a deep fake video of NASA'a administrator admitting so.

Maybe I'm missing your point?

(*) unless the hacker hacked me directly

But the signature can't really guarantee the truthfulness of the content. I could make a signed post that claiming that the Earth is flat.
important point, but in a federated or distributed system, ~~this~~ signed posts/comments may actually be highly beneficial ~~for~~ when tying content directly to an account for interaction purposes. I have already seen well-ish known accounts seemingly spoofed on similar looking instance domains.
distribution of trusted public keys would be an interesting problem to address but the ability to confirm the association of a specific account to specific content (even if the account is "anonymous" and signing is optional) may lend a layer to of veracity to interactions even if the content quality itself is questionable.
edit: clarity (and potential case in point - words matter, edits matter).
- Sure, but that has little to do with disinformation. Misleading/wrong posts don't usually spoof the origin - they post the wrong information in their own name. They might lie about the origin of their "information", sure - but that's not spoofing.

Among other problems, people knowingly spread falsehoods because they feel truthy.

The problem is people. We're all emotional but some people are just full on fact free gut feel almost all of the time.

Deepfakes are about impersonating the person in the video, fake news is.. Well, just someone lying. Signatures are meant to verify the source of information, not the contents of it.

Simple example, we can be nearly 100% confident that the person posting tweets under the Trump account is (atleast authorized by) Trump. Doesnt stop him from lying nor uploading a deepfake video.

The problem is the chain of trust. What tells you that the key you have is the right one and not a fake interposing between you and the real one?

That has been a problem for a substantial amount of time.

I could see it working if (say) someone tries to modify or fabricate video from a known news source, where you could check the key against other content from the same source.

I think I get what you mean, but validating the origin of a particular piece wouldn't do much for verifying the content. So such of the misinfo that's put out is taking some small snip of a broader story and reframing it in a way that makes the situation out differently.

This already exists in theory, although not many companies or products are implementing it: https://en.wikipedia.org/wiki/Content_Authenticity_Initiative

I think Leica cameras can sign their images, but I don't know if any other cameras support it yet.

Well one reason is probably that signing your article content to help it be verified when it is repackaged elsewhere is kind of the opposite of what news sources are trying to do with their paywalls.

How would key signing prevent deep fakes?