Those dirt roads are always remote, and often forbidding. Flash floods are common. Cellphone service is restricted to about 10 percent of the monument. In high season, Bureau of Land Management ranger patrols have to pull one stranded car a day out of trouble and they have to mount one full-scale search-and-rescue effort a week, on average.

Visitor services like those are “chronically underfunded and therefore understaffed,” I was told by Kevin Miller, a B.L.M. ecologist who has worked at the monument. Though the number of visitors to the monument is climbing, budgets are declining further, he said. A stop at one of the visitor centers for guidance on road conditions is essential.

This was the last area of the continental United States to be mapped, Mr. Miller told me. Trailheads may be signed, but the trails themselves usually aren’t. They are not maintained, and often they aren’t on maps, either. “The visitor experience is intentionally different from what people expect at a national park,” he said. “The Grand Staircase is really a wild place. It’s easy to get in trouble, if you’re not prepared.”

We stayed out of trouble during our visit, though the climb back up this route generated plenty of sweat. I was here to hike with my college-age great-nephew on a trip through southern Utah. A day exploring the flanks and waterfalls of this gorge, and the trailless crags above them, was a fine introduction. The extreme temperatures of winter and summer keep many visitors — estimated at more than 870,000 a year — away, but spring and fall weather are usually welcoming.

Later, I inquired at the office of Senator Orrin G. Hatch, Republican of Utah, who had urged Mr. Trump to rescind or cut back the monuments. “To this day, the Grand Staircase proclamation remains among the most flagrant abuses of presidential power I have ever seen,” he responded. It is “suffocating economic development and uprooting the lives of thousands of Utahns who relied on the region’s resources for their very survival.”

The senator’s analysis puzzles Suzanne Catlett. She is president of the Escalante-Boulder Chamber of Commerce, and the owner of a local restaurant, Nemo’s Drive-Thru. The economies of those two hamlets — the gateways to the monument — have been prospering on the tourism they draw, she said.