Uhura's job in the original series was effectively that of a Navy "radioman." They basically ran the ship’s official comms: sending and receiving fleet traffic, keeping the radios and teletype running, logging everything, and following very strict procedures. They didn't sit there listening to enemy chatter or translating languages. Intercepted/foreign-language stuff was handled by crypto techs, usually working in locked-down spaces and answering to intel, not the ship’s ops chain. In short: Radiomen moved the messages; CTs figured out what the other side was saying.
In that job, it makes no sense for Uhura to need to be a linguist, especially given the universal translator et al. In fact, Uhura explicitly says, "Cryptography is working on it, sir," in "Balance of Terror," so we know there's a department for that.