Age is trying to avoid being an infinitely-flexible swiss army knife like GPG. It's been argued that GPG's do-everything design is the root of many problems both technically and in usability:
https://latacora.micro.blog/2019/07/16/the-pgp-problem.html.
Minisign is a good similarly-small tool for doing signatures + verification of signatures and nothing else. The cryptography is similar, but the use-cases are often different. The tools both follow the UNIX philosophy of trying to do one thing well. Blenders and belt sanders both operate with motors, but no one tries to combine them into one tool.
>I also don’t understand the “anything to do with email” line. Sending my public key to a recipient on an out-of-band channel and then sending an encrypted email should be completely agnostic to the underlying encryption tools, no?
Yes, you can do that.
Age doesn't want to involve web-of-trust, keyservers, key rotation, forward secrecy, post-compromise security, message repudiation, signing, email standards, and email client integration. All of these would be necessary for a good end-to-end encrypted messaging system. Try reading about the Signal protocol to see everything it does, and then try to figure out how to stuff it all into existing email systems. It's hard enough to get any of that stuff right even without the restriction of working inside email.