Why did no Independent American Indian states ever develop?

I am answering only one of your questions: How come no native American states have formed?

Arguably, some states have formed.

Paraguay: According to Wikipedia, 90% of the population speaks Guaraní.

About 95% of the people are mestizo (mixed Spanish and Guaraní Indian descent. Little trace is left of the original Guaraní culture except the language, which is spoken by 90% of the population.

Bolivia (officially the Plurinational State of Bolivia):

Since Bolivia was created as a state on its own in 1825 it has been a multiethnic society. As a result, Bolivians tend to treat their nationality as a citizenship instead of an ethnicity.

...

In Bolivia, a 62% majority of residents over the age of 15 self-identify as belonging to an indigenous people, while another 3.7% grew up with an indigenous mother tongue yet do not self-identify as indigenous

Nunavut (part of Canada): above 80% of the population identify as Inuit, and Inuit is an official language.

Comanche Empire: Author Pekka Hamalainen argues that

In the eighteenth and early nineteenth centuries, a Native American empire rose to dominate the fiercely contested lands of the American Southwest, the southern Great Plains, and northern Mexico. This powerful empire, built by the Comanche Indians, eclipsed its various European rivals in military prowess, political prestige, economic power, commercial reach, and cultural influence. Yet, until now, the Comanche empire has gone unrecognized in American history.

Sequoyah (proposed state of USA in early 1900s, blocked by Congress, area now part of Oklahoma) is mentioned in another answer.

These states can be defined as "native American" on a demographic and/or linguistic basis. If you look at the question historically, you could probably argue that the states were set up by Europeans. However, as a lot of the available written histories were probably written by Europeans, it could be that there is an inherent bias blocking us from seeing these countries as "native American" (I will not argue for any of these points of view here).

In 1905 there was an attempt to make an entire "colored" (iow: Native American and freed slave) state in the United States. Sadly, Congress did not go for it.

Today the American Indian tribes (aka: Nations) are in fact still in existence, with their own laws and elected governments. They even occasionally have their own election contraversies. Many also have their own tribal property, with their own soverign police forces. They are immune to many state laws, which they tend to take full advantage of, by opening tax-free stores and casinos (to the extreme annoyance of the State governments). They also on occasion conduct their own foriegn policy.

However, all tribal members are also USA citizens, and for the vast majority, quite proudly so. After generations of living in both societies, most tribe members today identify themselves strongly with both nations. So in general, their members don't want to be a separate nation, just their own nation within the USA. Thus it is now really socially impossible for the USA and its Indian nations to ever disentagle themselves from each other. This state of affairs is what Osage anthropoligist Jean Dennison has referred to as "Colonial Entanglement".

If you are interested in what a Native American constitution would look like, Dr. Dennison's book Colonial Entanglement also has several historical Osage Constitutions displayed in their entirety in its appendices. Fascinating reading.

Moving into speculative fiction, Eric Flint wrote a series of books that investigate what might have happened had the Five Civilized tribes managed to set up themselves an actual independent nation, before they got hopelessly "colonially entangled" with the USA. The first few chapters of the first one is viewable for free here. It has some interesting things to say about the difference between organizing a Nation based on self-selected tribes (as the First Nations tended to do) vs. Race (or supposed "blood"), as European societies tended to do.