I don't know how the HSM/HSC(cv) COs are interacting w/ CAGs on deployments, etc, but as for the possibility of one of them being CAG some day, the argument against that using the night Case III with strained nerves, etc, doesn't work for me. It's just as much of a mismatch for a FW CAG to be calling the shots for a $45M MH-60R (plus 3+ crew) struggling home w/ low whatever pressure as it is for a RW CAG to be calling the shots for a $60M Rhino (+1-2 crew) struggling to get home for whatever it is that makes jet sphincters tighten. Whatever the case, I'd expect the respective squadron leadership to be in the room too, and a good CAG would call on the advice as appropriate.
When it comes to calling the shots and literally or figuratively leading the wing to make strikes (or whatever big movements the wing is doing), I think it's more nuanced than just "RW pilots can never hack it." HSM/C pilots on CVs who aren't taking the opportunity to get smart on what everyone else in the wing does are pigeon-holing themselves. We might not be there right now, because a generation of pilots have been in HSL and on the CSG sidelines, but once current HSM DHs are up for major command, maybe one will be there. Might be better than the worst RHINOWSO has seen.
I'd say that the CV area FW leadership that I mentioned is important because 90% of the cycle is FW tacair. And by that, mostly if all F/A-18 of some flavor. Is that to say that the reverse isn't also true (ie FW CAG doesn't know about RW considerations)? Absolutely not. But by the numbers, most everyone is in a Hornet of some flavor, and many are also alone and unafraid in a single seat jet without a built in book reader, or in the FNG position, built in sanity checker.....unlike RW who is going to have someone with experience on the ICS I'd imagine. Without going down a minutia rabbit hole, I'd just say that a VFA CAG is going to have a better handle on what the majority of the airwing is doing compared to an HS/HSC/HSM or otherwise RW CAG.
I can't speak to the O-5+ level of RW aviation, but I do know that the vast majority of O-2 through O-4 RW aviators I knew had literally no clue what we do beyond a very rudimentary understanding of the launch/recovery process. As a guy who stood XR with typically a helo XP, it was almost always me acting as interpreter for VFA considerations, whether that be the tanker plan, or really anything else beyond that involving spares or in country flow. That isn't to make the job of romeo sound important......it absolutely was un-needed IMHO, but I did get a general sense of the helo understanding of fixed wing, and it was basically nothing at all. No slight against them, it isn't their job, and my understanding of RW ops was abysmally small as well, but in terms of facts, that is what I saw. I'm sure the ideal would be that they would have a solid understanding of other communities like tacair, but that is not what I saw (and same could be said about VFA when talking about RW)