Fighters are good for air combat, but the question is, do they provide the service their cost implies? JSF costs 67mill USD, perhaps more. Their primary weapon, AMRAAM, costs 300k USD a piece. They are flown by pilots needing extensive and continuos training, every hour of which puts a strain on airframe. Air wing of 48 JSF's alone will cost some 3200 million USD at least.
Now, a SM-6 are more expensive than AMRAAM's, costing some 2 mill USD a piece, but can engage targets at virtually same range as realistic JSF sortie and over the radar horizon using outside target information. SAM's can also respond to massed attacks easier, are easier to keep in readiness and do not require pilots to be put into danger. (Although with UCAV's this is a moot point) SAM's can also fight ballistic missile threat which fighter aircraft cannot.
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.
Secondly, no SAM ship can carry its own AEW and ELINT support.
Yes, but technology has leapt since E-2 was introduced in 1964, 43 years ago. Today only the radar transmitter and power source need to placed onboard aircraft, while back-office duties can be handled somewhere else. A helo UAV AEW is only an example, aerostat option is also viable.
The problem with helo AEW is not its lack of space of electronics but the limitations of a helicopter.
1.) Slower speed, it can't get to its patrol station as fast as an E-2
2.) The higher the helicopter goes, the less efficient it is. At high altitudes, their is not enough air for its rotor blades to cut through forcing it to work harder. This limits the helicopter's range and altitude. For an AEW aircraft, altitude is one of its key components, the higher it is the farther it can "see" over the horizon.
3.) Design- it is very awkward to put a radar dome on an aircraft with a large rotor on its top. As a result, a compromise is made by installing it on its side and bottom. This results in a smaller radar dome.
E-2 Radar Dome
Sea King Radar Dome
Farther the ocean they are, more right you are, but every mile farther from targets means less sorties and less payload on target.
You are forgetting aerial refueling that is available to carriers. A missile is subject to the same constraints. Russia's long range missiles were as large as aircraft. A 25,000 ton Kirov were can only carry 20 of them.
I certainly agree carriers are not a bad naval investments all. The question is, whether they are optimal investments and whether carrier really has a long term naval role. Remember that during late 1930's quite much everyone in naval business was quickly procuring battleships. Battleships were useful during the war, but it may be well asked whether they were ultimately needed.
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.