The correct answer to this open question is the following.
What caused the Five Tribes and other American Indian tribes to change course and seek statehood for the Indian Territory was the constant policy of the United States federal government of continually dividing and destroying the Native American Indian tribes. This policy was known as "Allotment."
Native American Tribes in the Oklahoma Territory started to insist on the idea of seeking statehood for its territory after the Land Run of 1889 and the Organic Act of 1890. The Native American Indian leaders worked hard and elaborated four drafts or plans to specify statehood for the Oklahoma territory.
Unfortunately for the US Congress never passed any law that would have considered this NativeAmerican Indians' idea.