The handles that attach to the neck also allow me to not have to shrug my shoulders when I carry cylinders. Holding the valves, I often have to (as I dive sidemount typically and no, I don't put handles on them for obvious reasons - just a single tank configuration which I rarely dive). Your idea, which does have merit, would probably be worse for me.Think outside the box... Make a T-handle and some cord to slip over/around the valve (like the old school ski boot carrier)... it is removable. I also like the XS Scuba Carry Sling with a handle (carries horizontal)...
YMMV