Public key cryptography is used in many applications. What’s the motivation for using encryption tools in a transport protocol for signing data or documents? It’s not a full solution, and makes the SSH code base larger, and harder to maintain.
GPG has key management tools and various functionalities around signing. Minisign is another clean tool to watch for.
I use an ed25519 GPG key secured in a hardware security key. It’s convenient and secure. My SSH keys are ephemeral as much as possible.