Aviation is global, and we still need to interop with countries and airports that still use actual teletype. So the legacy protocols still remain, even though much of it is tunneled over IP links now.
Also: The keyboards used in both airplanes and in ATC facilities are often special reduced-footprint keyboards without shift/caps keys. (They're also often ABC layout rather than QWERTY.) So there's that, too.
However, AFTN (used for disseminating flight plans and weather between ATC facilities) still uses landline modems running TTY-originated protocols.
In the US we've moved moved off AFTN in favor of AMHS/X.400, as have most countries - but my understanding is there's still some last holdouts that haven't fully switched over.