If you need to project power across the world without them you need to be keeping countries "sweet" ad infinitum - hence the outlandish "foreign aid" budgets people whine about all the time.
Carriers, and war canoes in general, are not as independent of friendly shore facilities as you might expect and probably have as much need as do aircraft.
The fleet train needs to be resupplied. Spare parts are often delivered by air. Dockyards are needed for essential repairs. If someone manages to blow a hold in the side of your ship, or you run into a rock, or bend a periscope things can get a bit fraught if there is not friendly state withing reach.