This would ensure a more 'joined up' Air structure
But its aim is to serve the Army so handing it over to 'Air' is a step in the wrong direction. Fairynuff, it may get better looked after but I doubt it. The 'Air' command would view it as a burden and do you really think it would get equality in the world of fixed wing and FJs?
The only thing that needs to happen with JHC is to ensure the 'C' actually means Command. As has been said, it doesnt operate like a command, it operates as a Quango with pointless layers of 'management'.
The original aspirations of the JHC was to make it almost like the 'fourth service' but in reality it just became another layer of bureaucracy and a place where people 'disappeared' for a couple of years for no apparent reason.