You think that 3 x 40,000 modern designed UK built, would be more expensive to built, operate/crew than 2 x CVF CATOBAR, 2 LPD & 1 x LPH?
I think c40-60 F35b on 3 x 40,000t with 3 runways & 6 lifts will beat a similar number on 2 x CVF with 4 lifts & 4 cats.
I think you are confusing sortie rates with combat effectiveness. More of one doesn't necessarily mean the better the other.
You could buy 10 hulls based on a single-screw bulk carrier that can each operate 14 F-35Bs. Won't make them any more operationally effective/capable than 2 x CVFs.
Your super-LHD isn't optimised for the kinds of
sustained fighter operations a dedicated carrier is. LHDs don't have the kinds of aviation fuel and weapons storage as CVs, as much of that space is given over to or compromised by troop accommodation, the well dock and vehicle/troop access to it, landing craft accommodation and vehicles/stores decks.
Only superficially is an LHD similar to a CV, with a flat deck and an off-set island. Even the
Invincible-class weren't designed for sustained combat operations, it was designed as an escort carrier for the North Atlantic. The fact that the RN used them as such and made it work is a credit to the RN and the Harrier.
Secondly, while one of those super-LHDs is passing through refit, and one is tasked with amphibious operations, you have one last compromised platform available for combat fighter ops. One super-LHD or one CVF? Which would you want?
Only rarely (and through a sustained, pre-planned effort) will all three super-LHDs be available, which means that for any given operation there will likely be only two super-LHDs available.
Thirdly, I would also think that a short-notice swing role between carrier ops and amphibious ops would be undesirable*. Instead of being practised and (hopefully) excellent at their specialised role, it would end up with crews that are good (or even average) at both. Let the carrier crews work on their fighter ops, and let the amphibious crews work on their amphibious ops.
The only reason to go for the super-LHDs is if you do not think your defence budget can support 2 x CVFs + dedicated LHD/LPDs. Which is perfectly valid. But if you think it can, then why would you compromise?
* Someone is going to bring up the USMC LHDs, aren't you? Their LHDs aren't being used as the US's primary strike platforms, that is the role of the CVNs. The LHDs specialise (and practise and exercise) in the close support of forces deployed ashore.