You could trust the authenticity of the fact that someone used the author's key to sign it at some point in time.

You could not trust any claims the author makes about the circumstances under which the signed object was produced. They could have put their signature on a deepfake. They could have put their signature on the work of someone else. The author could have lost their signing key. It could have been created much earlier than it was signed.

A signature tells you very little about the thing being signed besides the fact that it was signed.

I never thought I would say that you could use a blockchain to solve something, but here I go: you can solve the timing problem with a blockchain.

Alternatively, you can go old school and publish a fingerprint in the New York Times or something.

The other problems remain, of course.

How do you protect the signing key?