Originally Posted by
ITA Hacker
It turns out there are a lot of very out-of-the-way places in the world that you can get to by airplane, and for many such points A and B you need more than three flight segments to do so...
Absolutely correct. Any two places that are not international gateways in their countries take at least one segment each to reach such a gateway. The entire set of international gateways in the world is not connected by nonstop (or even direct) flights; there are many gateway pairs that require at least two flights from gateway to gateway. Q.E.D.
(Local example involving two places I've been recently: Martha's Vineyard, MYY, to Punta Arenas, Chile, PUQ.)