PAGE, Ariz.—On a recent June afternoon, 18-year-old Aaron Diggdon positioned himself at the edge of a 1,000-foot drop-off at a natural attraction here called Horseshoe Bend—so his father could take some photos for Instagram.

“Anything for the shot,” said Mr. Diggdon, a college student from San Francisco, who posed for several pictures with the blue-green Colorado River winding its way around a sandstone escarpment beneath him. Several other people perched nearby on the edge of the canyon posing for photographs.

A...