What you described IS WHY age is the better option.
GPG's keyring handling has also been a source of exploits. It's much safer to directly specify recipient rather than rely on things like short key IDs which can be bruteforced.
Automatic discovery simply isn't secure if you don't have an associated trust anchor. You need something similar to keybase or another form of PKI to do that. GPG's key servers are dangerous.
You technically can sign with age, but otherwise there's minisign and the SSH spec signing function