An Homage to Teotihuacan

The Aztecs had proto-writing, which is to say that they couldn't write down a complete Nahuatl sentence, but they generally could identify proper nouns and action verbs. For example, you could describe an event such as "we attacked Texcoco, and defeated them, and forced them to give us tribute" with a glyph for your city, a glyph for an attack, a glyph for Texcoco, and a glyph for tribute, with orientation indication who attacked whom and who gave whom tribute. The Indus Valley script and the Quechua quipu are other examples of proto-writing, although the exact extent of what they recorded is under very vigorous dispute.

It is not clear that the Teotihuacanos had no writing system despite the lack of durable preserved forms (Stelae, etc) that other contemporary cultures used. In fact, the city of Copan was a client state of Teotihuacan and Copan had ample evidence of a writing system in common use. There's also clear indications of extended contact with Maya, who likewise possessed writing systems. So certainly teotihuacan was exposed to writing systems for centuries, and the contact was with peer or subject states with whom teotihuacan typically if not exclusively held the dominant power position.

The absence of evidence for Teo possessing its own writing system could be due to a number of factors. For example, there may have been a rule against engraving it on anyting durable, and it was only used on material that preserved poorly or not at all in the 15 centuries between the collapse of the city and the onset of archaeological investigation at the site. It may be that all evidence of it had been looted ORD effaced deliberately bye an internal change of power hierarchy, or by subsequent incursions into the abandoned city by successor powers. It's worth considering that the name Teotihuacan is not even the name that the original inhabitants used for the city (which is unknown to us except indirectly through Copan's reference to it in the Altar Q origin story) , but a moniker given to the site by the Aztecs nearly a thousand years later, who knew little to nothing about the original inhabitants.