The best way to take out an air threat is with an aircraft period. You are forgetting certain aspects such as initiative, mobility, and preemption. While the SM-6 can engage targets at such range, it cannot destroy them at their air bases, shot them down through offensive counter air inside their territory, or mess up a strike force's timing through interdiction. It can't attack a air strike group from a different axis. A SAM, once fired cannot be refueled and rearmed and brought back into a fight. Finally all SAM inherently suffer from the disadvantage that they always start their fight at 0 elevation and 0 altitude. An Amraam fired at altitude and at high speeds can double its range.
Yes, naturally SAM's cannot strike at enemy air fields, but that can be done with land attack missiles and bombers. Carrier borne fighters do not have that much range to act as air interdiction planes. Furthermore, as carrier borne fighters are tanked by other fighters every tanker sortie is away from fighting ability.
For action against air threat, let's consider two operational scenarios with two defending forces. First is a CSG air wing with 48 JSF's and E-2 AEW support. Second is a SM-6 equipped ships with E-2 equivalent AEW support.
Now, to give CSG a head start let's say it has received an advanced warning
of enemy strike operation. All of it's JSF's are fuelled and equipped with 4 AMRAAM's. As it does not know the exact moment enemy will strike, the CSG commander has decided to keep a four plane CAP along threat axis, some 100nm' away, where the E-2 also is. This will demand total use of some 12 JSF planes. Rest of the 36 are armed and ready.
The enemy approaches at 50m height, the E-2 keeps 9000m height. It can thus spot the enemy 225nm's away due to radar horizon. At this point, the enemy is 325nm's away from the carrier. For calculation purposes, the enemy aircraft are SU-34 Fullbacks, capable of Mach 1 speed at sea level, or 660kts.
Each enemy has 2 Moskit ASM's, capable of 65nm range. Thus time before enemy can launch it's missiles is 23 minutes.
Onboard carrier there's frantic activity. A fighter is launched at every 30 seconds. This means the last JSF is in the air at H-5, which means even the last plane launched can launch it's missiles against SU-34 which has not launched it's ASM's.
The fight is brutal. All in all, the 40 JSF's in the air are capable of throwing 160 AMRAAM's against the enemy. Some will hit, some will not. If the enemy has escort, it is well possible that some of the JSF's will get shot down.
You have to note that for this good performance the carrier has had to stood down it's strike operations to arm its entire air wing for air defence.
Now, let's match this performance by SM-6 equipped ships. The object is to match carrier air wing performance by placing 160 AMRAAM seekers into air within range of enemy, before the enemy has a chance to launch its missiles.
Two DDG-51's will be able to perform this task with AEW support. If AEW remains on station above the DDG-51's, again the detection is at 225nm range. After the launch, which can take place well within a minute, the interception will occur within minutes. More realistically, as it is uncertain any enemy will have 160 aircrafts to throw against USN, the AEGIS ships can wait at leisure to see which missiles have hit and which have not.
Now, let's take an another scenario. TU-22M Backfire equivalent planes with AS-6 Kitchen equivalent missiles. TU-22M's max speed at 50m's is 660kts. Range of AS-6 is 161nm's. In case of CSG, the distance from detection to missile launch will be 164nm's, or 15 minutes. While four CAP planes can have their try at Backfires, rest of the JSF's will have exactly 15 minutes to get launched and to get into a firing position. Maybe first two will, meaning a total fo 24 launched AMRAAM's against enemy missile carriers.
The SM-6 equipped ships, however, have time not only to launch against missile carriers but also to get a second shot against those which haven't been hit.
Secondly, no SAM ship can carry its own AEW and ELINT support.
Yes they can, if the capability of heliborne or aerostat. The capability may not be as good as AEW airplane, in heliborne case, but can be compensated via use of more platforms.
Moreover, with ultra-long-endurance missions there's less and less reasons to have these capabilities as shipborne at all. With 50h missions its feasible to keep a land based aircraft at station even literally almost half a globe away.
The question here is not whether a carrier is a bad investment but whether air power is a bad investment. After all that is what a carrier is, a moving floating airfiled. Considering that the fastest and most effective way to deliver ordinance on target is an aircraft, I don't see that change anytime soon.
No, its just that tactical fighters are getting rapidly obsolete as a way to deliver ordnance to target.