Simple answer to your last two points (intercontinental air and sea-based missiles) is that they can't replace the capability provided by CVs. Neither option is especially responsive to immediate demands or requirements, and both lack the visible deterrent factor that naval air can provide (although the B-52 has a similar capability, you still have the response time issue).

There has always been talk of the "risk to surface ships," but I've yet to seriously see it appear outside of the writings of theorists and those with various axes to grind. And as overseas bases continue to disappear, the CV gives us a capability that can't easily be replaced or replicated.

Just my $.02.