No big deal and a waste of a phib. They still have no organic air to air refueling, AEW, or ASW. They do not have the range or persistence of a true carrier. Worst of all, they cannot keep up with a carrier battle group. It's far better for CVNs to operate with the British and French carriers that can keep up and truly supplement the CBG.
I think you're equating the LHA with an actual supercarrier. A large escort carrier from World War Two (Sangamon or Commencement Bay classes) would be a better comparison. CVEs were able to project force locally, provide CAP and CAS to amphibious forces, and operate in somewhat lower threat environments (sometimes). If that's how these LHAs are to be used, then we're looking at CVE roles, not CVN roles. Using F-35s for local air superiority would not likely be a problem, and they and the LHA's helos wouldn't be operating so far afield as to need much in the way of aerial refueling, and there are always buddy refueling pods like the Hornet carries. If you want to see how creative one can get with a small carrier, just research how the British equipped their Illustrious-class ships. Helos for AEW? Yep, and reasonably effective, too.
For myself, I would like to see a somewhat higher speed for transit purposes, but that wide hull just won't allow for it. The extra horses needed to drive it a few knots faster would be exponentially hard to achieve.