It's not that people don't trust the Air Forces to provide adequate air. Its that they don't trust that when it isn't dedicated, during certain parts of the fight, that the Air heavy ACCs will prioritize it correctly. Therefore they want their own.
As I've said, the accuracy of the modern weapons and the flexibility of delivery has given the commanders the capability to directly strike the adversaries center of gravity at a time and place of their choosing. This is an incredible strength of modern air power.
However, that isn't always the tool required. When other commanders are the supported one, and the ACC is supporting, those other commanders want control of the assets as part of their plan, so they aren't assuming too high risks. Ironically, you've reinforced the concern with this chain of posts: "the best way to employ CAS is to retask aircraft going to strike other targets." Problem is, that leaves the priority decision to some faceless Air guy on the ACC floor.
This isn't new... its been going on ever sense the advent of operational air power. Strategic vs operation vs tactical: heavy bombers in direct support in Normandy and the resulting problems, tactical air in France and how deep they should be allowed to interdict, weight of effort in Vietnam between supporting air and strikes against the north. In the first Persian Gulf war there was a realization that Air had become precise enough to in effect win the operational battle, and ever since the USAF's mantra has been "everything to support the operational air plan." The continuing undertone that guys in contact want, in this order (my understanding, again I'm not a CAS guy), Apache, Cobra, A-10, Marine Harrier, Marine F/A-18, USN F/A-18, Strike Eagle, (Spectre somewhere in there but I'm not sure where) and then whatever else is available. The unfortunate lack of support from the USAF for Joint STARS, as its forte is battlefield interdiction and direct support of the Air-Ground war, and the USAF don't see those as core roles, and they don't think J-STARS is a very good ISR platform (I've had long talks with JSTARS on this subject because NATO AGS, where I worked for a while, is a J-STARS like Global Hawk... the Air types think its a horrible ISR platform but then can't understand why it could be given up to the Army or Navy for surveillance ops, even though it is Alliance Ground Surveillance).
Everything you are saying about the operational use of Airpower is correct, and its an incredible tool. But when Commander's have planned for direct support of their maneuver plan they want direct support, not support at the discretion of the ACC, because they are assuming the risk.
Edited to add: There's two reasons I care about this subject: in NATO at both AGS and Targeting I was at the heart of these types of discussions, and too many Air types are literally willing to give up everything else to enable Operational use of Air power, leaving us with only one tool; and my home community, MH, has been withering on the vine because good chunks of the RCAF don't care because its not their core role, and good chunks of the RCN don't care because they don't control it.