You would use it to add a dimension of time to the signatures. This allows for revoking/replacing keys while still keeping past messages valid. At work we've ben implementing a system like this where an identity is made up of a hierarchy of keys.
Let's say you have 2 key pairs as part of your identity. You sign a message with key 2 and publish it on the blockchain at block height H. Then at some point in the future, you lose the private part of key 2 or it becomes compromised. So now you sign a message with key 1 that says "replace key 2 with key 3 from this point on" and you publish it to the blockchain.
Now, any messages signed with key 2 before the replacement can still be deemed valid, but any future messages signed with the compromised key will not be valid.
If one needs proof of existence features, bitcoin already delivers this trustlessly at scale: https://opentimestamps.org/ You merkle hash effectively limitless data into a single bitcoin transaction. No need to spin up a new (and likely inefficient blockchain) to do notary tasks.
Proof of publication Trustless time stamping Trustless transaction execution.