Story time: Back in 2013 I was on a trip with a group (from this board) and we did have one guy get 2 flats on the same trip. Actually, he didn't just get 2 "flats", on two separate occasions 4 days apart, the tires actually ripped to shreds on the sidewall while driving at a moderate pace (25 - 30 MPH) on a graded dirt road. I can't remember if he was running LT or P rated tires but it was a real eye opener. BTW the tires were Hankook Dynapros which is why I will never consider that tire again (I actually had a set on an old 4runner years ago.)
The biggest problem he had was that we were in a very remote part of Nevada. Three days after the first blowout, we got to Tonopah, NV. He went to a local tire shop to see if he could get a replacement tire and they wanted something like $300 or $400 for one tire - something crazy. So he elected to wait and then the next day another tire shredded itself. So now he had no spare. Fortunately someone else on the trip had the same model of truck and loaned him a spare tire and he took off to the nearest town (Bishop, CA) which was a couple of hours away and had 4 new tires put on there.
Anyway - somebody here mentioned carrying a spare TIRE but not a spare WHEEL. Had this guy had a spare TIRE he likely could have had a local tire shop change the tire out for $50 - $75 while he waited. But if they have to SELL you a tire, you're going to pay top dollar if they even have your size, and if they don't it will likely be at least a day or two before they can get one from a warehouse. So in that circumstance, it might actually be prudent to carry a second spare tire only.