For military use, the fact that you do not need consent of third states to use their infrastructure and can support operations on the other side of the globe directly, is golden.
Remember the Yom Kippur War in 1973. Everyone who helped Israel was subject to Arab oil embargo, AFAIK including countries that just allowed American Israel-bound planes to land and refuel.
Similar things may happen again somewhere around South China Sea.
The human ego. Rich people.
Also, the "global" nature may lend itself to container ship salvage or search and rescue. Esp. if the Starship doesn't need to turn around immediately, I can see a market for that.
All of these seem like they will need special-purpose custom Starships operated by a non SpaceX entity.
also, in a much darker turn of events: organs for billionaires and political leaders.