Even if you accept the idea that two CBGs are sufficient for a Taiwan Straits (I don't, let alone the idea that they could be both available and on station in time), you're out of your mind if you think they're sufficient for the conflagration thereafter.
You say the number of decks should be 13, and that the mission requirements (low sortie rates) could be met by a QE class.
Well then: stipulate a drop to 10 CBGs, and a relative sortie rate of Nimitz:America class of 4:1; QE:America 2:1.
F-35Bs/tactical UAVs off perhaps a dozen ESGs get you there, with a big chunk of the other overlapping capabilities that you'll need for the same likely mission in the package already. Figure STOVL and strategic UAVs into the picture as well.
With these deck numbers the smart course is to regulate the rate of production of Ford, not start over with a QE design. Even if down the road you decide you need a QE built around EMALS, the less risky evolutionary path is to build it in numbers in big decks first.
A USN small deck CATOBAR today is a solution looking for a problem.
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