Just a few quick points:
tdracer/Wondering
The UK intends to operate a joint RN/RAF force, this is not tied exclusively to the carriers. For conventional CV aircraft that would mean a high training burden to keep everyone carrier qualified. In 1982 1 Sqn RAF were able to embark Harrier GR3 aboard HMS
Hermes because they are V/STOL aircraft, and because the ship was up to speed with operating jets.
Additional catapults and arresting gear mean more expensive equipment to be integrated and maintained, and more manpower. The SDSR 10 cuts slashed naval manpower without much thought, Cameron wimped out of increasing RN (and RAF) manpower in 2015.
Lastly, STOVL carrier operations are less sensitive to whether than old style CV ones. The QEC design is smaller than the US carrier and would have not had the same operating limits with F-35C, however with F-35B they probably can.
Easy Street
One possible NATO scenario puts a UK carrier based ASW task group (with NATO frigates and SSKs) in the Eastern Atlantic and/or GIUK gap to conduct task group ASW (Merlins with dipping sonar, frigates (and destroyers) with towed array (and hull mounted) sonar and submarines as part of the task group. Meanwhile the F-35B can counter Bears, Backfires, and so on.
See:
Fire and Ice - A New Maritime Strategy for NATO's Northern Flank
The UK has committed a carrier capability to NATO, and this seems similar to the Cold War and the roles of CVS/Sea Harrier/Sea King.