WEBF, what I am saying (and I assure you I'm not conveniently ignoring), is that yes on a particular day Strike won't be the primary mission but even so, the quantity of ac may not be sufficient to do it alone. Therefore, if the QE is acting as the air base for assets conducting ASW, etc, then it will have to be in conjunction with other AD assets: T45 and probably other carrier-based air and/or land-based air.
People seem to forget that this aircraft has some great all-mission capabilities but some amazing niche ones as well. Those niche capabilities are going to drive the JTFC to pull them for his Strike plan and, quid pro quo, apportion other (less-niche) AD air (F-15/16/18/Ty/Rafale) to provide the required screen for QE and other ships/helo/amphibious doing their business. Now, if the mission is entirely minesweeping, that's different but also unlikely. If the mission is entirely about Amphib, I agree totally with you, but getting Marines ashore against a near peer enemy will require a LOT of battle space shaping BEFORE any air can get near the coast.
The thing to bear in mind is ensuring flexibility but please remember: in the Joint fight, the Theatre Air Defence Plan is entirely CFACC's call, not the ship's skipper's, whose concerns will undoubtedly be made clear to him via the MOC to CFMCC. The only time you really need to be a self-licking lollipop is when you're alone and unafraid AND in range of the enemy ("who has a Navy and an Air Force..."), which should never happen. If you're underway/en-route 1000nm from the AOR, the jets probably can't reach targets anyway so yeah, skipper asks CAOC or other agreed C2 agency to assign assets to Air Defence or training sorties.