There very few places in the lower 48, even in the SW, that are 100 miles from pavement. Even 50 miles. I've been to a few, and I carry extra spares and a patch kit, but still...
Alternately, your putting on a spare that's just as worn as the one that just gave out...

20 years ago I did an all-dirt, Mexican border to Utah border trip across AZ. Being poor, I started this journey on well-worn BFG AT KO's (avatar picture is from that trip, trailer full of supplies, parts, tires, and mountain bike). I had lots of flats (4, including one on a precarious incline) due to the nature of the road and the worn state of my tires. I'd rather have a 10 year old , full-tread spare under the car than one with 45,000 miles on it already. 8-10 year old tires just don't magically blow sidewalls after a certain date. But that's just me, and apparently my risk appetite is off-the-charts for this group. I even (gasp) run a smaller spare than my 275/70/17's, because you know what? Torsen says it's not a big deal. Lots of conflation here with viscous coupling Subarus and other AWD systems that just don't have the same risks for imagined "drive train damage" as our rigs do. Assuming you use a spare for it's limited purpose (I do.). I know there's some that won't accept that, and say "just in case, I will never take any risk > 0.0%). Guess what? Your tranny might blow anyway, even though you've used a 5 tire rotation for the last 14 years...
Less over-thinking, more wheeling...