I'm going to discuss why your question is a bad question.

Its main problem is that it is of the form "Why didn't X happen?"

In history, we generally study causes and effects, so logically the relationships are of this type:

A -> B

A will be the conditions that obtain to cause writing, B will be the development of writing. Now A is actually a set, you could go away and study each place/time where writing developed, and for each case you could say factors X, Y, Z caused the development of writing. If you found in every case that a certain X was necessary, you could tentatively extrapolate and say something like "X appears to be a necessary factor", though not a sufficient one.

Your question is more like

A -> -B

Which is fine in logic, but not in history. Because you're asking why didn't something happen, which it is technically not possible to discern.

I understand your type of question, it's one that naturally occurs to us. So let me elaborate about the two ways of investigating this type of question.

1 -You can study a sweep of instances where writing did develop, and interrogate those causal factors, and assuming there is some degree of commonality, make some hypotheses about the type of factors necessary.

Let me stop and say: history isn't Sid Meier's Civilization games. There isn't a universal tech tree, there's no transcultural 'progress' towards 'modernity'. The idea of history as progress is ideological, not historiographical.

Assuming you did 1, you could then investigate:

2 - Were there other historical contexts that looked similar to those in which writing developed, that did not develop writing. This is even more tentative than 1, but you could make some arguments about 'inhibitory factors', if you found some.

History wants to understand why things happened the way they happened. Asking why things didn't happen the way they didn't happen is a very difficult question that always involves far less confidence, because whatever X, Y, Z factors you find in approach 1 that explain the development of writing, it's always possible that an entirely different set of factors, J, K, L, might exist that would lead to writing. History is explanatory, not speculative.

On your particular question, here are better questions:

1. What evidence of writing is there across the Americas?
2. What was the role of orality in Native American cultures?
3. How 'universal' was the development of writing?

To be fair, Sequoyah did invent a written language for the Cherokee in the early 1800's.

Obligatory Note: "Native Americans" encompasses two hemisphere spanning continents and more than 10,000 years of human history. As /u/talondearg notes, asking "why" something happened presupposes that it must happen. This factors which lead to the development of a particular cultural artifact are unanswerable with parameters set as widely as "Native American."

That caveat said, writing did develop in that enormous scope of territory and history you posit it did not. Mesoamerica is in fact on of the very, very few areas where writing arose independently. The Cascajal Block attests to the presence of writing some three thousand years age in the area.