That's only the beginning. Over about 3000 years Sumerian cuneiform was used (at least) by the Sumerians of course, a language not related to any other as far as we can tell. Then Akkadian, Babylonian, Assyrian, those 3 are semitic languages.

Also used for Elamite, another contemporary language not related to anything.

Hittite, an indoeuropean language. Again completely different from all the others.

Urartian, which I can't recall right now what it is related to but it's not semitic

and finally, heavily adapted, Old Persian, another indoeuropean language.

And it's not trivial to just use Cuneiform for a different language as the "letters" don't fit the sounds. For example it's a pain to map cuneiform symbols to Hittite sounds and uncertainties remain in transcribing and translating the texts.

What's more, we can only read, translate and even to an extent speak those millenia old languages because the writing was used so long and was still used for languages where we have modern descendants and/or texts in different scripts and alphabets like the Rosetta stone or the Darius inscriptions.