Many Cherokees stayed who did not desire to live under Indian government. Many settlers were part-Indian.
When the Red Sticks attacked Fort Mims and killed all the troops and settlers, most of those inside the fort were “breeds” as were many of the attacking Indians.
There is a lot of Indian blood in white Americans but due to the stigma of the important people of the time, anyone who could pass for white did so and their ancestry was lost. In the frontier moved westward there was always a shortage of white women because there were no “malls” or good schools (or whatever was important to women at the time) on the frontier. Pioneers make do and there were a lot of mixed Americans.
I grew up near the Northern Cheyenne Tribe in Montana and the last full-blooded Cheyenne died in the 1980s. Eastern Montana is still very empty and many Cheyenne, man and women equally, intermarry with the local whites. I myself dated a Northern Cheyenne girl and my sister dated a Cheyenne boy in high school. They are a very good looking people.