They allow you to project power, as the saying goes, anywhere in the world, for extended durations, without needing the permission or assistance of any friendly

They allow you to project power, as the saying goes, anywhere in the world, for extended durations, without needing the permission or assistance of any friendly nation (i.e. airstrips in a nearby country) [0]. If you're going up against any nation that doesn't have the ability to sink an aircraft carrier (which is almost every nation in the world) they are very far indeed from obsolete. [0] So long as you have a serious logistics chain and serious support vessels including protective warships; if all you actually have is one aircraft carrier, you're going to find it pretty useless for long-term power projection.