The 22DDH and its sister will be just as you say, and they definitely will have a possibility for naval air arms in the classic sense. No one will argue that the Kuznetsov and particularly the Liaoning are not designed to carry a significant naval air arm with a fixed wing capaility designed in from the onset.Its primary purpose is as an aviation carrier, and should thus be compared with other similar vessels of the PLAN.
My bottom line, is, for the purposes of Jeff's comparison of VLS capable destroyers and frigates, Hyuga shouldn't be included
The Hyuga and the Ise are both designed to be very large, anti-submarine destroyers. They are dedicated to that task and have the arms consistant with it. They will not have, and have not been designed to have a naval air arm with the purpose of attacking other surface combatants or ground targets.
So, I have essentially treated the Hyuga like I would the Haruna or Shirane classes which the Hyuga class are replacing. Which is to say they are all large destroyers, with a very expanded rotary aviation capability for the purpose of hunting subs, like any dedicated ASW DDG is. In doing so, they also act as a task force leader in the hunter killer role to protect capitol assets and sea lanes from submarines, and to protect themselves and other members of their group from hostile air threats. In fact, the original intent and main purpose of the JMSDF in the cold war with respect to any major outbreak of hostilities was to provide a huge capability in that reagrd for US carrier groups.
Now, the 22DDHis a different horse IMHO. They have decks designed to handle jet blast, they have cleared the CIWS away from the landing and take off areas of the deck, and have added a side elevator with a much larger hanger. Clearly, IMHO, they are meant to be able to take on a fixed wing component.
But the Hyuga cannot...and will not. She is a dedicated ASW helo carrying destroyer...with a flat deck. Even though she carriers "aircraft," they have a specific purpose consistant with ASW DDGs, and in that regard she can never, and will never be able to be like the Liaoning and the Liaoning's basic function.
Anyhiow, that's my reasoning. Certainly others can and will disagree.