I'm not ticket off since I knew it didn't have one when I bought it.
Since I bought a Tahoe Hybrid in 2008 I've also driven without a spare for 7 years now. But unlike you, I drive both my Tahoe and S out of cell phone coverage, and on remote gravel backroads (mostly this one):
Google Maps
I think my luck must be wearing thin but I'm knocking wood here.
My snap reaction is that that road is a clean one, therefore your statistics make sense to me. (To me clean means not only free of nails, pointy rocks, debri, etc., but also no potholes, sharp weird turns, geological formations in the roadway itself, other vehicles, other people in other vehicles likely to make it unclean and/or unpredictable, etc.)
Compare that to San Jose where I drive all the time: there are at least an average of two major potholes I hit every day, because Santa Clara County never fixes them at all. I've chewed through 10 rims in 2 years, and had a dozen flats. Also, the "road diet" communists in city and county hall are installing road-colored concrete curbs everywhere, in the middle of lanes, on every side of lanes, that you have to drive around constantly, and are completely invisible. These types of "road diet" obstacles have killed many people who have been hit by other people who crash into them after losing control after hitting one of these invisible road diets. Of course, they cause all sorts of vehicle damage, not the least of which is seriously damaged wheels. Sometimes, you get out of a brush with them with a very lucky simple flat tire (of a type a patch kit will never repair). I've avoided most of these myself using a "high-beam-only" policy whenever I encounter those types of obstacles at night, and immediately and always divert to another road that doesn't have them, and go back to highbeams only when there are no other vehicles. But it's yet another source of flats. Also in urban areas, there's lots of garbage that isn't innocent on tires. And finally, on my last long distance trip, I had to avoid 3 debri spills that could have taken out car parts including a tire (one was listed on Waze and two were not); I had both the following distance and reaction time capability to avoid all of them safely and calmly, but it is just one of those reminders that sometimes these things come up, and what if someone did zip around and cut me off and blind me to the hazards before I hit them?
So, I think your beautiful dirt road is a lot fancier than you imply it is.
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Do you carry spares for every other critical piece of the vehicle? What makes the tires so special?
I spend a LOT of time outside of cell coverage in the mountains, often on gravel back roads. Still never needed a spare tire in my life, I've patched a few, but never changed one. I don't plan on lugging around that much extra weight, and taking up that much extra space, all for something that I've never needed in my entire driving career. I've been stranded by more dead batteries in my life than flat tires, and I never carried a spare one of those.
Second post from a rural Canadian who says they rarely get serious flats. I suspect my initial gut reaction extends to even more of Canada: your rural roads are relatively clean and good quality!
EDIT: And now I've seen a lot of USA urban drivers post, saying they get numerous flats, which leads me to believe that many urban areas have a lot of ghetto-garbage and ghetto-potholes causing flats. I've also seen many urban drivers post saying they don't get flats. I kind of recognize the urban areas that are worse at flats have more ghettos than the places people post from that aren't getting the flats. If you live your whole life in a city with nice roads and no messy people, you'll never get a flat, whereas if you live anyplace with potholes and nails, you'll get them all the time. I see this also happening to some people who are in the rural areas in USA, which leads me to believe that rural areas in USA are given to poor road maintenance and cleanliness, compared to our neighbor to the north. All this means is that people's different experiences all make sense.