Although, many has pointed out (in this thread and others) the disadvantage of heavily armed carriers and the reason why US navy didn't adopt such an approach.
But if we look at the US navy again, the US carriers are escorted and protected by large number of destroyers and other type of ships. Of course this is a good tactic, but it is extremely expensive and to maintain that vast amount of ships and a carrier is very difficult unless you are a nation that is very rich and had huge number of warships at your disposal.
The reason a USN CV is lightly armed is that her aircraft are her main armament. You can't be firing off missile etc and conducting flight operation. It just does not work well. That's why the USN has escorts with it's CVNs. They form the Carrier Strike Group
Actually, the US carriers carry a fairly heavy self-defense armament. They are not armed for offensive fighting themselves, because as popeye indicates, their aircraft are more than adequate for that, carrying much more firepower, longer distances, and more accurately.
But for self defense against air threat (aircraft or missiles), the armament has developed into
2 X Medium range Sea Sparrow Launchers with 16 missiles ready
2 X Short (but very effective) range RAM launchers w/42 missiles ready.
2 X 20mm CIWS Phalanx systems
Those are pretty strong armaments and allow for a lot of self-defense for any missiles or aircraft that get through :
1) The aircraft defensive ring of carrier aircraft far out from the carrier on barrier CAP.
2) The AEGIS escorts on picket and outer ring air defense duty.
3) The AEGIS escort(s) on innner ring air defense.
The aircraft carrier and its airwing are far too expensive a commodity to risk needlessly, meaning, to risk without having the absolute best defenses available as they accomplish their mission to project power and defend the interests of their nation...which itself is a risk, which is why their escorts and their own onboard self defenses have to be very strong. Having most of the defenses centered on the carrier itself would not allow for the defense in depth her escorts help to provide. For this reason, I expect the PLAN carrier to constitute the centerpiece of a CSG that is just as large, if not larger that the carrier escort group.