I understand the concern, but I think the spare tire is the last vestige of an earlier era.
When I was a kid, our family car always had a box in the back with spare parts: belts, points & plugs, coolant, a couple quarts of oil, etc. And they got used regularly (as did the spare). Our vacations often involved multiple full days of driving and I can't recall a single one in which something didn't go wrong with the car. Three days stuck in Paducah waiting for parts. Another three in Portland. Four in Vegas (my parents always talked about that one like it was their own little slice of hell - stuck in a Vegas motel room with four underage kids and no car - and 104° daytime temps). Before my time, both my parents and grandparents had stories of having to buy a replacement car in the middle of a trip when their old car died. Fun times. And as for tires specifically, thanks to the Firestone 500 debacle we once had 6 flat tires on a single trip, all of which were un-patchable. Another time, we ran over a board in the road that apparently had a nail in it. The front right tire, rear right tire, and right tire on our trailer were all flat. The spare didn't do us much good for that one. Even during more normal driving, it wasn't unreasonable to expect about one flat tire a year.
Thankfully, those days are gone. It's not that things don't go wrong anymore, it's just that they're so much less likely that it isn't worth it to haul around spare parts. A few years back, we drove 8,500 miles across the country and back in our Jetta Sportwagen without a single mechanical issue or flat tire. And in the last 25 years, I've had just three tire issues, two of which were such slow leaks that I was able to add a little air and drive on them to get them patched. The third was a bigger deal, but even it was a perfect candidate for a can of fix-a-flat. Again, it's not that flat tires never happen, it's just that they don't happen appreciably more often than any other automotive failure these days. We don't carry around spare parts for any of those other failures, so why carry around a tire?