The agglutinative languages (common throughout Asia) have in common an approach to communication, but they are difficult to relate to one another. What little is known of Elamite comes from bilingual texts, and betrays agglutinative structure, but the two most ancient native written forms remain unreadable. Elamite, like Sumerian, is considered a language isolate, and unrelated to each other.
Even if such languages share a common origin, it's not unlikely that they are inherently more changeable even than other well-attested non-agglutinative (Indo-European, the most widely spoken language family) languages, making their common origin(s) difficult to discern, even by native speakers (or especially by native speakers).
Harappan is only known from the body of texts, and none of the proposed "translations" have been generally accepted (reminds me of the huge numbers of "solutions" to the DB Cooper case). In an extreme case, a few years back, one research team claimed that their computer analysis showed that Harappan wasn't a written language at all.
The fact that Dravidian has survived and classical-era inscriptions are known (including in some Roman Empire sites on the Red Sea) and yet it hasn't emerged from the Harappan texts suggests (obviously doesn't prove) that they are unrelated. Lack of horse imagery in the Harappan remnants probably means the language (or languages?) of the Harappans was not Indoeuropean, either.
Yes, I know I don’t have any basis in fact for that guess, but it just sounds so perfect a theory - “oh people spread across the littoral”.