Because American understanding of indigenous peoples is not rooted in memories from history (interactions with tribes on the East Coast, for example), since almost all of that has been systematically white-washed and even today doesn't exist substantively in popular media or school curricula. Instead it comes from movies and tv shows about the "old west", itself a mythological creation, but one that bares some resemblance to the history of white settlement progressing across North America from East to West during the mid 19th century especially (mostly superficially). This mythological setting was brought into being through numerous fictional (and some fictional but allegedly truthful) narratives in first print, then as stage shows, then in film and television, which became wildly popular from the end of the 19th century when such tales described semi-contemporary events up through the mid 20th century (and to a lesser extent even today).

These stories and depictions bare little relationship to the real history of the times and places they were set but many people casually fall into the assumption that background details in such stories are broadly accurate, and when they are shared across many other stories this reinforces that belief. However, the "wild west" setting did not exist as it was depicted, it's no more real than Narnia.

In general compelling stories need aspects of conflict and danger, and one source of such that was ready to hand was the Native American tribes of the great American plains. Of course, there was some truth to the conflict and combat between white settlers and indigenous tribes during the late 19th century, but again the portrayal in these narratives was simplified, mythologized, and transformed into exaggerated and ridiculous stereotypes and caricatures.

One particular type of entertainment worth spending a little more time on here is the "Wild West Show". Part travelling carnival, part variety show, part pseudo-museum, part dime novel come to life these started out with "Buffalo Bill" Cody doing tours around America and Europe. These were wildly popular and created a perception in the public of a reified "Wild West" that was predominantly fictional, including displays of natives who were part of the show, some of whom were actual Native Americans, almost all from the Lakota tribe. They were "dressed up" in exaggerated fashion for the shows (for example, the women were put in skimpy clothes and elaborate headdresses they would never wear traditionally). These depictions cemented the "indian" look for Westerns in later Wild West shows and other Western genre media as well as in the public conscience. Much like the rest of the "Wild West" mythology it became a self-reinforcing feedback cycle. By the 1950s, for example, a "Western" film was not some novel work of art, it was referencing (explicitly and implicitly) a whole lineage of western tv shows, films, comics, literature, and wild west shows stretching across an entire century. Stereotypes of Native Americans had evolved and become effectively standardized by then.

And those depictions largely still exist in the popular culture in the present day, having failed to be replaced by more historically accurate portrayals of natives due to the continuing poor quality of education on the matter, especially in US K-12 education.