Well, let's look back at ancient cultures as a model.
Before the first couple of centuries AD, many of the European and Asian cultures were oral only. They had spoken but not written languages. As late as 700AD, monks were still creating some of Europe's written languages so that they could translate the Bible into the local language. I know of 1 Saint who did this for the Slovakian language around 700AD.
In many of these clutures, memorization became a PRIZED ability. Someone who could "memorize" and repeat what they had heard or been told, was considered QUITE intelligent. So a good memory was a sign of intelligence.
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Other then that, Hypothetically...
We MIGHT still have math, since your question only mentioned "writing" and not math. So maybe with computers, we'd convert to a binary language. 010111010110110001010110101011011011100101
Who knows.
Maybe we'd use picturegrams to depict our ideas and communicate.
Maybe we'd slip back into a truly dark era, with the illiterate being taken advantage of by those who CLAIM to be able to read. I can see where "relics" from the past might be "interpreted" by those who supposedly know how to read them and these Scholars might read tot he masses and tell them what to do and think.