The wide variety of existing planes was in fact a choice of three: F35C, Rafale or F/A18 Hornet.
Hornet while upgraded and still good today, is ~40 years old design, and not a sensible choice for something expected to be in service for another 20-30 years.
So actually a choice of 2, and one of those is variant of the F35.
The QEII carriers are still working up, so arguably, not having a full complement of F35B is not a major issue. In the meantime, they can do the same role as HMS Ocean did (retired, and was always supposed to be a short term measure) as a helicopter carrier: the Wildcats, Merlins and Chinooks work just fine.
So good enough for 'show the flag', counter narcotics/counter piracy and disaster relief. i.e. all the things that the Royal Navy actually does day in and day out (Wars being thankfully somewhat rarer).
The new carriers of course replace the old Invincible carriers. Which were designed to operate the Sea harrier.. so could fly only one specific type of aircraft.
It's just possible that the RN may have some idea of what it's doing when it comes to naval aviation: without looking anything up:
First to take off a fixed wing aircraft from a ship
First to land ditto
First to kill a pilot in the attempt
First full length aviation deck
(First to install steam catapults? note sure on that one)
Invented the mirror landing system
Invented and proved concept of angled flight deck (USN first to build a carrier with one)
First to land a jet on a carrier
Invented the rubber flight deck (yup, really, Didn't work out)
First to take a carrier into a shooting war
First to lose a carrier to torpedo, ditto gunfire, ditto air attack
First to use carrier air power for air to air interception, ditto land attack, ditto attack of ship at sea, ditto attack of ship in harbour
First to launch a heli-borne amphibious landing (Nope, it wasn't the USN)
First to deploy V/STOL to sea
First to use V/STOL at sea 'in anger'.
First to deploy helicopter AEW (I think)
First to have a carrier attacked by modern missiles
There's probably some other stuff they came up with too.
So if the RN wanted F35C and V/STOL carriers, I'm not going to argue.