The designations are not purely political designations When you compare the Arms built into there hulls too say the Kitty-hawk class a True carrier. You find that both the Japanese and Chinese/Russian carriers make concessions too there air complement by placing the priority on internal armament. The Russians were very honest in there Designation for the Heavy Aircraft Carrying Cruiser, They have on two occasions begun or designed a true carrier Project 1153 Oryo and Ulyanovsk Although the Ulyanovsk would have been still more armed then a American carrier. the Varyag as intended even included ballistic missiles mounted in the middle of the fore deck( missiles that would have meant securing any aircraft near that location in event of firing and took up space in the hanger deck preventing use of that location for storage or maintenance). Now she might have been a Inferior Cruiser too say the Kirov battlecruisers but still better armed then there American counterparts That actually well out weighted her.
The Hyoga in design is still an evolution of the Japanese model of DDH still armed as a Destroyer just packing more aviation assets.
How is hyuga an evolution of Japanese DDHs?
And I'm sorry, but hyuga is "just a destroyer with more aviation assets". It's a helicopter carrier with some good self defence capability. That's it.
I understand that the armaments of a ship and previosu design philosophy leading up to a ship may influence what we call it.
You could say Kuznetsov is an "aircraft carrying cruiser" or the kiev class as well. But in a comparison with other navies, they would not be included as "cruisers" but rather "aircraft carriers" or "helicopter/VTOL carriers" for kiev.
In the same way, hyuga, despite its 16 Mk 41 tubes, and whatever DDH ancestry it may have, would not be included as a "destroyer" with the likes of atago, kongo, akizuki, or 052D, 052C.
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