That may not be the plan right now. But I expect that to be the long term result. In the age of cruise missle warfare, the way to survive is to be fast and stealthy
There are at least three development paths - some designs will combine parts of all three [Warship design is always a compromise]
1) Armor and other passive defenses. This includes damage control, internal divisions and redundancy. This is the ability to avoid cheap 'mission' kills - and even absorb major damage and continue operations. We no longer build armored ships [BB & CA] but we still have a few in mothballs.
2) Stealth - or as Monty Python once instructed 'how not to be seen'. SSN / SSBN designs are pure stealth platforms.
3) Active defenses - Radar, missiles, guns and emerging directed energy technologies. The intent here is to do unto others _first_.
The Navy already has plans under consideration for small aircraft carriers built on much larger versions of this type of catamaran hull. Each carrier would only handle 6 to 12 planes or helicopters, with a large force having multiple carriers.
My background is in the 'surface' Navy [FFG / DD / DDG] not the bird farms [CV / CVN / LHA]
This has been an argument since before WWII.
It resurfaces periodically in the professional literature. In a way, the Navy does have many small aircraft carriers - each ship with a Mk41 launcher system can launch dozens of aircraft [harpoon, tomahawk]. For that matter, the FFG7 class was called an 'air capable frigate' during the design phase - large flight deck, two hangers.
The size of a CV / CVN design is constrained by the performance of the aircraft it carries. With today's engine technology [pushing thermodynamic limits] a catapult launched, conventional landing aircraft has a greater payload fraction [range, endurance, speed] than V/STOL designs [A/V8B Harrier] I'll withhold judgment of the F35 until they're finished designing the naval variant.