I believe any smaller US carrier would most likely be as large as the Queen Elizabeth CVF. There are sound reasons why the British CVF is its size...
From beedall.com Navy Matters website:
It was recognised that size is not directly related to costs - the Royal Navy demonstrated (and not just to its own satisfaction!) that a large ship is not only cheaper to build in terms of cost per tonne but also has lower maintenance costs.
There were soon four principle size drivers influencing the CVF design. First, the sortie generation is clearly related to the number of aircraft and therefore the size of the hangar, emissions, and aviation support. Second, there is the provisions of the ‘for but not with’ capability, for example allowing for the fitting catapults and arrester gears determines the length. Third, there is the overall complement required to be put in the ship, particularly given the more generous spaces for sleeping and recreation now required for all rates and ranks. Finally, there is the tankage volume necessary for unrefuelled range at the cruising speed. There are others, but those are the most important points.
The large size also provides the greatest possible deck area, which not only facilitates aircraft handling but also allows the incorporation of large magazines and fuel stowage. Magazines will in fact have a significant impact upon ship size and costs. However the larger hull sizes will create some operational and support problems, for example a lack of suitable dry docks, which could be expensive to resolve.
Certainly a large ship would ensure that (unlike the Invincible's) that there's plenty of room for mid-life update and expansion, and in an emergency the carrier could carry a much larger "surge" airgroup than normal.
The STOBAR CVF design was eliminated in January 2001, at the end of Assessment Phase Stage 1, but the two competing carrier contractors (BAE Systems and Thales Naval) continued to develop designs based on operating STOVL or CT