Most of these systems started out as teletype printers, back in the day. The teletype systems only had an all-caps character set.

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.