I wrote my MA thesis about the coexistence of Mesoamerican writing systems! I think a better question to ask here is why would Central Mexican people adopt Maya writing? Why does anyone need writing? There's an assumption sometimes that phonetic writing is superior to all other forms of graphic representation and that once a community comes into contact with a community using phonetic script then it will spread. Writing is a culturally specific technology that fulfills a social function, and because different cultures have different needs and priorities, their communicative and representational media will differ. The Classic Maya used writing to record primarily the birth, accession, and death of their rulers on stelae, but other Mesoamerican people may have had different priorities regarding their representational systems. You bring up the lack of writing at Teotihuacan, but they actually do have what appears to be a complex system of symbolic notation. Whether or not this can be considered "writing" is a more theoretical question that depends on your definition. Regardless of whether we count it as writing, the Teotihuacanos clearly knew about Maya hieroglyphic writing but decided that their own method of representing information was adequate for their needs. I recommend you look into Colas' 2011 article on Teotihuacan writing as a starting point.

There has been a fair amount of research into indigenous American writing systems beyond the Maya and Their Way of Writing provides a really nice overview (it's actually the book that actually made me decide to pursue a PhD in non-Maya Mesoamerican writing). It's also worthwhile to look into the Postclassic period more deeply, as this was a time during which multiple representational systems coexisted and mutually borrowed from each other. People in Oaxaca and Central Mexico created manuscripts contemporaneous with the Maya codices recording religious and genealogical information in a complex semasiographic script. Despite the similarities between these manuscripts, such as some shared glyphs, they still maintained distinct regional traditions (see Boone 2007, Boone 2008). At the heart of your question is the assumption that phoneticism is best, but I think that once we really consider indigenous American representation outside of that assumption we can begin to understand why some communities may pass on phoneticism in favor of another form of representation that better fits their cultural needs.

Boone, Elizabeth Hill 2008 Stories in Red and Black: Pictorial Histories of the Aztecs and Mixtecs. University of Texas Press, Austin.

Boone, Elizabeth Hill 2007 Cycles of Time and Meaning in the Mexican Books of Fate. University of Texas Press, Austin.

Boone, Elizabeth and Urton, Gary (eds) 2011 Their Way of Writing: Scripts, Signs, and Pictographies in Pre-Columbian America.

Colas, Pierre Robas 2011 Writing in Space: Glottographic and Semasiographic Notation at Teotihuacan. Ancient Mesoamerica 22(1).

The assumption that contact with writing necessarily entails adoption of a writing system is flawed, as the spread of scripts throughout history has been uneven. Even in places where writing has been introduced we can still see an emphasis on oral traditions in certain cases, such as with the Vedic tradition in India, West African griots, and the focus on memorization and recitation of the Quran. Plato, even as he put the teachings of Socrates in writing, was not alone among the Ancient Greeks in opining that writing degraded memory by allowing the reader to rely on a text rather than their own mental prowess. In such cases, the transmission of knowledge orally is seen as more authentic, honest, and less prone to individual bias. Whether that is true or not is obviously debatable, but the implication is that anyone can write down "their" version of something, but someone giving a recitation of memorized verse or scripture can draw upon a long genealogy of transmission to shore up the veracity of their statements.

All of this is non-specific to the question at hand though, so let's focus our view by considering how rulership in Mesoamerican was exercised. Many conquering polities in Mesoamerica practiced what has been called "hegemonic" rule, in which the conquering state did not exercise direct control over the conquered, but instead largely left local political affairs in order so long as tribute flowed. This does not appear to exactly be the case with Teotihuacan and Tikal, since the dynastic records and isotope analysis show the seizure of rule by a group from Teotihuacan. This initial conquest group, however, appears to have rapidly intermingled with the previous elites and there appears no attempt to "teotihuacanize" Tikal or any of the other Maya polities which show evidence of Teotihuacano interaction. If Teotihuacan functioned as other conquest states in Mesoamerica, then what we would see is less an intermingling of cultures and more of a thin layer of Teotihuacano political dominance, which periodically asserted itself to secure the interests of the distant home city.

Cowgill (2015) finds it useful to distinguish between various levels of Teotihuacan influence. To tease out the difference between signs of Teotihuacano culture -- the people themselves with a shared language, religion, ethnic identity -- and the polity of Teotihuacan, which encompassed the areas under its direct political control. He further distinguishes between the actual physical presence of Teotihuacanos in outside areas, and its much wider influence, as shown by the emulation of Teotihuacan by polities outside the direct control or even regular presence of Teotihuacanos. At Tikal and several other Maya sites, we see evidence of direct presence and culture, but the nature of its connection to the Teotihuacan polity is unclear, with these cities perhaps never being under direct rule. The attestation of Central Mexican peoples intervening in other Maya sites presents an even more opaque picture, leading Cowgill to speculate that some depictions of Teotihuacan-style soldiers in Maya murals may have represented independent actions by Central Mexican settlers or other sorts of opportunists. Regardless, the picture we have of the connection between Teotihuacan and the Maya region is that a number of states in the latter region gave at least nominal recognition to the overlordship of the former, but overall the area was quasi-independent and what Teotihuacan influence there was quickly "went native."

The other thing to keep in mind is that while the Maya script is not as impenetrable as first appears, it has been seen as a "closed" system of writing, one that was altogether uninterested in adapting and spreading beyond the culture and language it served. Houston et al. (2003) note that examples of encoding foreign words into Maya script are exceptionally rare and occur only in the Postclassic, when Nahuatl was becoming the lingua franca of Mesoamerica. They point to "phonologically mangled diety names taken from Nahuatl" in the Dresden Codex as examples and further note that even foreign imagery was demarcated as distinct from the rest of the "native" writing. They contrast this to the proto-writing systems of Western Mexico which, while employing rebuses which may not translate, also use broadly understandable pictorial conventions which allow the paintings of that region to be broadly intelligbile across cultures.

So while Maya writing may have been a fully developed script, it was not one geared for ease of transmission and adoption by other culturo-linguistic groups. Further impeding adoption may have been stymied by the small number of fully literate Maya. Houston and Stewart (1992) push back against hypotheses that reading was confined to a small scribe class (instead classifying the skill as "uncommon"), but do endorse the view that the ability to write was an even limited ability. So only a small number of Maya could read and full literacy was contained to a very small group, most likely in specialist roles. We can see an example of this in the Maya barrio of Tetitla in Teotihuacan, which has gorgeous Maya-style imagery, but almost no examples of script (cf. Taube 2003).

There is, as already mentioned, the presence of proto-writing to the west of Tehuantepec, which may have further impeded adoption of a whole new system of script for abroad. /u/cdaviii has already covered this, so I'll just throw out a mention of Taube's seminal monograph on the topic, The Writing System of Teotihuacan.

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^(Cowgill 2015 Ancient Teotihuacan: Early Urbanism in Central Mexico, Cambridge U Press)

^(Houston and Stewart 1992 "On Maya Heiroglyphic Literacy" Current Anthropology 33[5])

^(Houston 1994 "Literacy among the Pre-Columbian Maya: A Comparative Perspective" in Writing Without Words: Alternative Literacies in Mesoamerica and the Andes eds. Boone and Mignolo, Duke U Press)

^(Houston, Baines, and Cooper 2003 "Last Writing: Script Obsolescence in Egypt, Mesopotamia, and Mesoamerica" Comparative Studies in Society and History 45[3])

^(Taube 2000 The Writing System of Ancient Teotihuacan, Center for American Studies)

^(Taube 2003 "Tetitla and the Maya Presence at Teotihuacan" in The Maya and Teotihuacan: Reinterpreting Early Classic Interaction ed. Braswell, UTexas Press)