It's a very pleasing image irrespective of vignetting. Individual taste I suppose will dictate whether you remove it or leave it: my taste is leave it.
You probably couldn't get a more atmospheric and "big sky" place to unleash a camera — any camera — than your location in the desert of Arizona. Most of us down here, Dowunder, would kill to photograph those places, among others, Monument Valley, Grand Canyon, Yosemite (and do it darned well better than Uncle Adams!!), Slot and Antelope Canyons... would be criss-crossing the USof A very frequently!!