Good to hear from you again FV.
A carrier with fighters would not just defend herself, but also the other ships and other forces in the area, hence the term fleet air defence. A bit like sending a ship with a particular weapon system will probably make that ship a priority target in some situations.
By "local air superiority" (not my term, it was a quote) I meant at ranges of 100 to 200 nautical miles or more, not point defence. I suppose the term local is relative, and was meant to suggest that even if their is no air superiority over the entire theatre of operations, the area around the carrier is afforded a degree of protection.