In recent years, a LOT of people have discovered the value of getting outdoors and enjoying nature. That's awesome, but it's coming at a steep cost. I saw a news story this morning about how crowds on the Appalachian Trail are exploding with images of erosion and other physical damage to the trail, trash on the trail, liquor bottles in fire pits and food stuff lying around everywhere (a fed bear is a dead bear). My "home trail" has gotten beat up by people cutting switchbacks and making "shortcuts" to the point that it's hard to see the actual trail in many places and it's now uncommon NOT to find the little doggie doo bags just tossed on the trailside (I'd much rather you just let the dog poo on the side of the trail, at least that will break down, but that's another post). Part of me would love to find a way to fix the problem but another part of me, probably the selfish part, just wants to find a place to go that's not beat up, littered and crowded. Is it just me? Are there any "unpopular trails" left to just walk out a few miles, hang a hammock or setup a tent or whatever (bivy, tarp, bedroll, etc.) and just be outside with no artificial noise, no artificial light and just unplug?
There are oodles of unknown, unfrequented trails....Do you expect me to popularize them? Weeell, maybe just a little bit....
At Channel islands NP, you can get a backcountry permit and check out the terrain, actually with no formal trails at all and probably no other visitors. Takes a fair amount of advance planning, especially with beach closures...
Looking at a trail map of Saguaro NP just the other day and I'll bet the trails to Rincon Peak, Happy Valley Saddle, and Reef Rock are sparingly used. You can probably check with any area's staff and get advice onTLF's (trails less frequented).
Honestly, as a longtime resident of Southern Arizona and avid hiker, backpacker and LNTB camper, the reality is with the increased popularity of camping, backpacking, hiking and RV’ing, because of Covid-19, even at the crack of sunrise, I will find some other vehicles at the trailheads.
As for myself, if I were to seek “exactly” what you have described, and being very familiar with the Sonoran Desert, local climate, terrain, and hazards, I would select a remote dry stream/river wash and follow it’s natural path.
During our annual Monsoon Season, the dry stream/river washes are mostly cleansed of any traces of human activity, with the water runoff from the surrounding desert, hills and mountain ranges.
Because of the large array of optical telescopes at Kitt Peak National Observatory, there are regional outdoor lighting restrictions, to minimizes their effect on the night sky.
Though the Sonoran Desert is a beautiful place to live, hike, backpack and camp, careful planning and being at least in “Code Yellow” on the trail or stream/river wash are key, to assure a positive outdoor experience.
Just to emphasize the last paragraph above, natural hazards, especially steep drop-offs, abound in many streams. Trails have been developed for many good reasons, especially to provide relatively easy, obstacle free passage.
Tanque Verde Falls, just outside NE Tucson, is ostensibly named for the waterfall there, but to me, the "falls "refers to the many fatal and near fatal falls that have occurred there over the years, including eight fatalities during one sudden flash flood in 1981. Floods can be a problem.
I get it. My favorite playground is the Smokies. While there are many extremely popular/crowded trails, there are tons of trails in the park that you can definitely find solitude and untouched trails from trash. When I lived there, I loved hiking the trails that people didn't tend to hike. Sometimes I'd be out there hiking for 14 hours and only see 1 or 2 people the entire day.
The Olympic national forest in North Washington is a fantastic place for this. The trail twists and turns and wraps around itself and even though it's fairly popular the people there are so spread out that it feels nice and secluded the whole time. The trail is well kept and visitors seem to have an appropriate respect for the nature they're enjoying. Personally, I prefer to follow the "leave no trace" principles, and many there share this sentiment. If that's a bit too far out for you, the hoe-river trail is another good option. The pacific crest trail I've heard is gorgeous, but I myself haven't been down that one.