Anybody who has served in any capacity with the Army where they contol air tasking understands immediately why they don't have air assets...they have no idea how to use them. They view air assets as an extension of the ground commander and tie those assets to his mission. To hell with all the other targets of opportunity with a more strategic affect. If the ground commander is in charge of air assets and has his way, the aircraft will be drilling holes in the sky above his mission doing nothing because they're "his" assets rather releasing them to another unit or tasking where they can have a greater effect. There is a reason the Air Force fought so hard to become a separate service, AND a reason the DoD and congress agreed it needed to happen. The same reasons are still applicable today.
So, in order to keep generals from hording CAS, we ended up with decades of ignoring CAS with aircraft that were pressed into CAS without being built for it, tasked by people that were more interested in strike missions, and with an extra couple of layers of command structure separating the people needing the CAS from the people doing it.
On long range vs. short range air superiority, one of the reasons that US fighters had a problem with Migs in Vietnam was that the long range US fighters were going up against short range Migs that had less baggage. We may well have lucked out there, because (to my knowledge) the US hasn't really defended against an air attack since WWII.
I think that is a pretty narrow view of things. Having the Air Force apart from the Army encourages a healthy discussion about the most effective way to utilize air power in a given environment. The army is always going to think it needs CAS when sometimes that may not be the most effective way to manage the battle space.
And lets be 100% honest, having the Air Force to blame lets the Army commanders off the hook in many regards. If the Army had its own aircraft and was responsible for using air in the battle space to a given depth from the front then they would run into the same issue as the Air Force can which is that there are more CAS request than one could hope to service. Given the chance most ground force commanders will call for air support all the time to help protect their force. Someone has to be the ******* that decides what priorities are.
I also think it is very unfair to say that CAS has been ignored. You can cite the Vietnam War about fighters and CAS but to be honest all US services were mostly preparing to fight a nuclear WW III and much of the equipment was designed to fight that war.
When a conventional posture was called for the USAF clearly took the steps necessary to provide CAS and by almost all reports I have heard has supplied the necessary CAS in both of our current conflicts. I mean in what instances can someone say the USAF has not provided the necessary CAS when called upon in recent history?
I honestly think the system has led to fairly good outcomes for both sides. The USAF brings a branch to planning that thinks about the battlefield in a deeper sense which is immensely valuable. The Army has, because of their restrictions, focused on systems such as Apache and UAV's that really provide what they want better anyway which is persistent fire support at the point of engagement and relatively deep within the division or corps area of responsibility.
Having two chains of command responsible for high speed jets in one battle space is a recipe for disaster as well. Under the current joint operations model all the army fixed-wing planes you want to give them would be under the command of the air-component commander to begin with. You are basically talking about undoing Goldwater-Nichols.