Where are the wildest places in the south-western US? By "wild" I mean places where evidence of people or their lasting effect on the land are minimal. Particularly, I am looking for places with infrequent airplane overflights, low night-time sky light pollution from man-made lighting, no signs of logging, or roads.
Any Wilderness Areas.
Seriously. The legal mandates for designating "Wilderness" in the US (as defined by congress) have very rigorous criteria established by each of the major land agencies. Take a look a the Forest Service process for an example.
Size, lack of roads, lack of altering (logging, invasive plants), opportunities for solitude are all defined criteria.
However, there are many empty stretches of land that are not Wilderness, and there are many Wilderness areas that are "Wild" by law, but not in reality (lots of visitors, close to civilization, etc.)
Now, which areas are actually the wildest? That is entirely subjective and dependent on where you go. Wander 1/2 mile off the busiest trail, you might not see a soul. Exploring a slot canyon, you might feel like the last person on earth, even though a highway runs parallel.
Often "wild" is a state of mind.
For your specific criteria, you might do best to start with a map of Wilderness Areas, find the center of the biggest one, overlay a map of city lights, and a map of flight paths and see if there is any green showing through the lights and flights...
(Though from personal experience, the majority of commercial flights are high enough you never notice. It's low-flying tourist flights that disturb - and many Wilderness areas have laws against this.)
Other than the airplane overflights, this will be pretty easy to see by looking at a map. I don't know why you care about stuff like commercial jetliners because they are 5-8 miles up, hard to see, and don't seem to bother wildlife any.
As for roads, looking at a map is a good guide. Few roads means few people, which means not much light pollution, at least nearby. In the southwest US, you're never going to be all that far from at least some dirt road. The more important criterion I think is how many people show up, not whether a road is nearby or not.
I would look at some of the larger patches of national forest. LBell is right in that the Wilderness Areas will have no active roads, but they tend to be small, so could have more light pollution from nearby populations and provide less of a feel of you being out in the wild because the not-wild places are closer.
It would help if you described more what you really want to do when you get to this wilderness. Do you want to be able to hike for days without running into anyone? On trails or bushwhacking? How do you plan to get there if you want to avoid roads? How far from the nearest paved road do you really want to be? How far are you willing to go? What about dirt roads where someone in a 4 wheel drive pickup might come along once or month or something? If all this really matters to you, then how do you want to avoid having you presence spoiling it for everyone else? If the requirement is some minimum distance from other humans, then obviously only a few humans at a time can have that.
I have been some places in the southwest where I was very likely the only human around for a few miles that night, and the sky was quite dark. One such area is in the Coconino and Apache-Sigreaves National Forests north of the Mogollon rim in Arizona. Other than Flagstaff to the northwest and Winslow to the north, there are very few sources of light at night and a lot of open terrain. There are some paved roads thru that area, and lots of dirt roads, but most of the time very few people are on the dirt roads. The vegatation in that area is also conducive to bushwhaking, which is pretty much just walking around wherever you want to. Getting away from where anyone else is likely to be within the next few months is really pretty easy. The major evidence of people in that area, aside from the dirt roads, is ranching. Some of the land is leased to ranchers and has cattle on it. Even if not, there will be the occasional barb wire fence or remnant of a old one.