It would be useful to list and analyse those few cases where writing was invented, i.e. were there any particular circumstances that were especially conductive to creating a writing system that weren't present elsewhere.

My guess would be that trade and territorial spread of the given state are very useful for inventing it, since it's needed to calculate and store data, to communicate across greater distances (sending messages to other towns that you trade or have some relationships with - not necessary in tightly-knit tribal communities)...

And once someone invents writing, which is a pretty difficult thing to do (especially to teach it to others and make it actually durable), it's obviously much easier for anyone who comes into contact with that culture (which is likely to happen if the culture trades a lot or covers a large territory) to just imitate and adapt their writing system rather than invent everything from the ground up.

This is ofc just my theory based on what I know about the Near East (e.g. Phoenician alphabet > Greek > Latin & Cyrillic).