Some friends of mine did Southern Tier. They did an indoor trip, no camping. Started in California, rode to Florida, rented a minivan and each day a different member of the group drove the van with their luggage and provided water stops while the others rode.

In the desert southwest, one of them had seven flats a day on average with his skinny tire road bike. That sounded horrendous to me, until I started reading some of the experience of others in this thread. Suddenly seven flats per day does not sound so bad. That said, I average one flat per year.

But one of that group had a total of four flats for the whole trip, he brought his Cannondale touring bike, had 35 or 37mm tires on it, I do not know what brand or model of tires, but they had better flat protection than the skinny road bike tires that some of the others used.

If you start considering sealant in tubeless, there was a thread on that topic recently on the randonneuring board.
Ready to give-up on tubeless road tires