As a native english speaker, I fully agree. Exile is something that happens to the rich and powerful, when they fall out of favor. It does not at all connote what’s going on here. Deportation is far more apt.

It’s from the early days of Greatest Gen, and references Captain DeSoto of the USS Hood (NCC-1703). DeSoto and the Hood made several appearances in TNG, and Ben and Adam leaned into his chill vibes, theorizing that the Hood would be a great place to work.

It’s also an allusion to the phrase Friend of Dorothy, an older euphemism for LGBT people.

I think it was originally jokingly conceived as a sort of passphrase or shibboleth for fans of the pod to identify each other without revealing their embarrassing enthusiasm to outsiders, e.g.

Q: “Are you a friend of DeSoto?”

A: “Best boss I ever had!”