Generally these things get planned in a way that means if certain things happen, other things can happen in response. There was no need for a carrier or RAF air cover for a routine evacuation (I'm curious as to why the OP feels it was needed for a ship, but has never been needed for many of the RAF led NEO in recent years?).
I know its easy to slip into fantasian dreams that somehow had HMS ILLUSTRIOUS had her flying circus onboard then somehow all would be well as the mighty GR9 would have kept the enemy at bay, but what if she'd been alongside, or in the Pacific or doing something else?
ENTERPRISE went probably because she happened to be the closest ship in the region at the time. Many different ships have done NEOs over the years - its not something you can only do if you have steely weapons and a rakish bow you know.
Why the bloody hell does this pathethic desire to slag off the Crabs come about at every opportunity by some Naval supporters? I've spent my entire adult life wearing Dark Blue and I am ashamed at the nasty cheap point scoring on display from the OP here - he does the RN an enormous disservice. You don't speak for the RN and I am glad others here can see that.