Carriers and LHDs may appear similar from the outside, but they aren't on the inside. The LHDs youy are suggesting will be used as carriers would all require F-35B, which will be the only operational (in service) STOVL jet for many years to come. AV-8B Harriers or Sea Harriers will not be available or provided to third navies. Hence, the concept of a LHD based mini-carrier revolves in its entirely around the F-35B. This too will not be available to all, not in the last place because of cost. As indicated, the Australian navy operates 2 Juan Carlos type ships and has studied what it would take to make them F-35B compatible. As a result of the studie, acquisition of F-35B was ruled out as too costly. I am aware Turkey will be adopting a similar ship and may decide to get F-35B with them (or at least have the ships prepared for them). Turkey, like Australia, is a level 3 partner in the F-35 program. Thusfar, Turkey - like Australia - has ordered only F-35A. Likewise Japan and South Korea. The only F-35B customers to date are UK and Italy (for the dedicated carrier Cavour: not an LHD design).
https://en.wikipedia.org/wiki/Lockheed_Martin_F-35_Lightning_II#F-35B_2
"Although the Australian
Canberra-class landing helicopter dock ships were not originally planned to operate fixed-wing aircraft, in May 2014, the
Minister for Defence David Johnston stated in media interviews that the government was considering acquiring F-35B fighters for
Canberras, and Prime Minister
Tony Abbott instructed 2015 Defence White Paper planners to consider the option of embarking F-35B squadrons aboard the two ships. Supporters of the idea stated that providing fixed-wing support to amphibious operations would maximize aircraft capability, and the presence of a
ski-jump ramp, inherited from the original design, meant that the vessels were better suited to STOVL operations than equivalent ships with flat flight decks. Opponents to the idea countered that embarking enough F-35Bs to be effective required abandoning the ships' amphibious capability and would make the pseudo-carriers more valuable targets, modifications would be required to make the flight deck capable of handling vertical-landing thrust and to increase fuel and ordnance capacity for sustained operations, and that the F-35B project itself has been the most expensive and most problematic of the Joint Strike Fighter variants. In July 2015 Australia ended consideration of buying the F-35B for its two largest assault ships, as the ship modifications were projected to cost more than AUS$5 billion (US$4.4 billion). The plan was opposed by the Royal Australian Air Force, as an F-35B order could have diminished the number of F-35As purchased."
https://en.wikipedia.org/wiki/Lockheed_Martin_F-35_Lightning_II#F-35B
Even with STOVL/VTOL jets, the difference between using an LHD for carrier role rather than using a dedicated light carrier os obvious. See example of Spanish navy ships Juan Carlos and Principe d'Asturias.
Principe d'Asturia
Displacement: 15,912 tons standard, 16,700 tons full load
Length: 195.9 m (643 ft)
Beam: 24.3 m (80 ft)
Draught: 9.4 m (31 ft)
Aircraft carried: 29 fixed wing and rotary wing aircraft
Juan Carlos
Displacement: 26,000 tonnes standard, 27,500 tonnes at full load
Length: 230.82 m (757.3 ft)
Beam: 32 m (105 ft)
Draught: 6.9 m (23 ft)
Aircraft carried:
AV-8B Harrier II,
Chinook,
Sea King,
NH-90
Aircraft composition:
- Pure combat: 25 AV-8B/F-35B + 6 flight deck parking spots
- Mix: 11 AV-8B + 12 NH90 + 6 flight deck parking spots
- Pure transport: 25 NH90 + 6 flight deck parking spots
FOR THE SAME AIRWING, the LHD IS 1.5-2x the displacement of the 'Sea Control ship' . So, if purely used for carrier role, the LHD is actually 'overweight' and 'oversized'.
Besides, USN carrier studies reveal that 1 large carrier with a big airwing is more cost effective than several smaller ones wich combained have an equivalent airwing. The carriers thems selved require a large sum total of crew, for example, and each smaller carriers would need its own escorts i.e more escorts needed > more ships and crews needed.