There are ways to do this, i.e. through custom protocol handlers. They could also be used to deal with following accounts on other servers without having to copy/paste all the time.

Mastodon had a custom URI for interacting with it, but it wasn't an opt-in feature and the constant prompt to register the handler annoyed people. That's why the feature and the protocol were removed and they haven't been added back.

I think it's rather silly to first ignore the calls to opt into the protocol popup, then remove it completely because there were too many complaints about the protocol popup, and now refuse to add it back because of "bad UX".