I just want to mention that more frames doesn't equal more capability. You have to carry the logistics to run a cetain level of tempo and have the pilots and crews to keep it up. Is there room in the hanger deck for more, yes. Is it going to equal more sorties and effective rotation, probably not. Cramming the deck isn't conducive of a fast sortie rate, it clogs the monkey works.
Remembering the days when decks looked like this...
http://www.history.navy.mil/photos/images/h97000/h97716.jpg
I will opine there is plenty of room aboard today's carriers before they would be "too" crowded...Note the 10 A-3s (out of the 18 embarked) on board the Indy.
It would take something on the order of 100 Bugs and Rhinos to match the deck factor the Indy sported in late 1960 (the pic was actually taken in Nov 1960).
...That said, you have a bit of a valid point. It was crowded in those days, and because of the plethora of manufacturers -not just airframe makers but the whole host of OEM parts makers that each aircraft company preferred-logistics was a nightmare. It didn't help that MTBF of most of the bleeding edge electronics systems could be measured in minutes in many cases as well.
However, having just 44 (relatively diminutive in size compared to the aircraft in the pic above...and CERTAINLY diminutive in terms of "legs") strike aircraft aboard -and a dearth of other special mission aircraft such as ELINT tanking and ASW- isn't necessarily the better place to be in terms of combat effectiveness.
First, there is an unstated assumption that combat losses will remain at the next to nil numbers they are today. It is an assumption just waitng to bite the USN (and USAF) in the A-- too.
Unlike late WWII where aircraft were expended at a prodigious rate, but were replenished just as quickly by CVEs shuttling aircraft forward...
http://www.ibiblio.org/hyperwar/USN/ships/dafs/CVE/cve99.html
...or as in Vietnam when attack aircraft losses in the hundreds could be absorbed...
http://en.wikipedia.org/wiki/Aircraft_losses_of_the_Vietnam_War
...the 21st century USN will have to pretty much finish the fight with the resources they start with, given the dramatically reduced unit levels and greatly diminished manufacturing capability.
Another issue is the assumption of "assured access" near the beach. If the carrier has to fight a littoral battle, and is forced to operate in contested areas while conducting power projection missions, numbers-not to mention people proficient in all the varied mission areas- of aircraft become very important very quickly indeed.
Related to this is, if an opponent can mount a robust enough sea denial strategy, the carrier may be forced to stand off at such ranges that the "modest" combat radius of the current flock aboard will very quickly stretch organic tanking beyond what it can handle, and may even stretch what big wing tanking can provide. Add in sortie lengths and effectiveness would plummet.
Which brings up the last point....The assumption that land based assets will always be able to "be there" when needed. Will they? If a country decides to shut down their fields or airspace, then the carrier will be hard pressed to even start a fight, much less stay in it...