I suppose the question is if POW was offered at a reasonable price and government wished to not only expand the ADF assault/long range strike capability, which way should the RAN jump?
It would be in a different league again. You would have a single example of a very large and unique ship with huge crewing requirements (which would be far more burdensome than the purchase price, which would be 2-5 times that of a LHD). Crew of 700 is closer to twice times that of a LHD, so you would be looking at laying up one or more ships (like frigates/destroyers/LHD) to be able to crew that. Then you have to ask the question could the RAAF put on another 2 or 3 squadrons of F-35B's to make use of a ship of that capability. Then would the Australian government be able to fund it adequately in times of peace and in times of war. The Army would quite clearly would be the loser, cause we would need to reallocate a few battalions of the army to the Navy and Airforce.
While I don't like to say things are impossible I think it is very unlikely. And the sort of situation where it might become available there would be an equal bet of the UK re-negging on the deal (like last time?).
And what does that higher level of capability buy you? It still isn't enough to compare to the level of capability US/China are working on. Regionally we could do what we needed to do with less aircraft than a QE. With a 3rd LHD, we would still have effectively up 3 carriers, so if we needed to surge capability (most likely in conjunction with allies) we would still be a significant player in that.
The advantages of a 3rd LHD being an off the peg purchase, with training, logistics, risks, support, Army amphibious value, sealift, HDAR, etc etc should not be undervalued. Expanding an existing pool is much easier and cheaper than establishing a new pool, by an order of magnitude. The value of flexibility in deployment, capability, crewing, upgrading etc is very high.
For the type of operations Australia is likely to be leading or contributing, a LHD is going to be much more useful than a full dedicated strike carrier of a single ship.
If we want to compare ships in a ball park way:
Canberra class:
Crew ~350 (~300 RAN, ~60 Army, 3 RAAF)
Cost ~$1-1.5 billion AUD
Amphibious force: ~1200 troops
Airwing: ~?8+ F-35B's + helicopters (25 max)
Trieste LHD:
Crew:~460
Cost: ~€ 1.1 billion ($1.75 Billion AUD)
Amphibious force: ~1050 troops
Airwing: ~10 F-35B's + helicopters
Izumo Class:
Crew: 970 total (inc airwing)
Cost: $1.2 billion USD ($1.7 billion AUD)
Amphibious force:??
Airwing:? 8-12 F-35 + helicopters (28 max)
USS America:
Crew:~1060 sailors
Cost: $3.4 billion USD ($4.43 Billion AUD)
Amphibious force: ~1600 troops
Airwing: ~20 F-35 + helicopters
Queen Elizabeth Class
Crew: ~680 not including air element
Cost: ~£3.1 billion each ($5.7 Billion AUD)
Amphibious force: ~250-900
Airwing: ~50+ F-35B's.
So if you need to support a lot of planes, then the QE is the one to go with. You could arm wrestle mid sized nations (like 1980's Argentina) with considerable ease. Smaller nations you would be so utterly dominant, you could exert US levels of diplomacy. You could slip in and replace US carrier power when required. Global power projection or full war intensity level of operations. America would give you significant capability, likely to overpower anyone in our immediate region without being reliant on land based air. Trieste is getting close to America sized deck and capability, it could in theory operate more than 10 F-35's. Izumo is a bit mysterious because its not in its final config.
In terms of Amphibious capability all a fairly similar (except Izumo). America is bigger, but has no dock. QE is significant, but has no dock. Trieste and Canberra are similar in overall capability and cost. Realistically Trieste, Izumo and Canberra are the only realistic options Australia has of a proven build type for some sort of amphibious/carrier ship. Everything else quickly spirals upwards in terms of cost, manpower and capability.