I also don't see how removing the ring will improve the comfort, since it only shapes the crown and has no bearing on the part that sits on your head. If we really want to improve the naval cap, I would say it would be better to adopt the USN design of a frame with a removable cloth cover that can be washed and/or replaced as necessary. It would look better (i.e. easier to keep clean) and be lighter and breath better than the current foam-lined plastic thing. I suggested this to the Maritime Clothing and Dress Committee a few years ago, but they didn't see the "need." Perhaps they "need" to wear their plasic hats in the sun a little longer? Or perhaps, they already have been? 
The big comfort-improver is ripping out the foam and other associated crud, and cutting out most of the stuff around the inside of the cap - leaving only the padded segment. Not sure if all that was supposed to keep it warm in the winter, but all it does in the summer is soak up sweat. Not really amenable to cleaning, either.
Only downside is the cap then develops a dent from your head - not noticeable when worn, but can be seen when it's off your head.
I've never looked closely at pre-unification white caps, but have the impression they're much more lightly built than the current item.
Maybe it's time to bring back two caps? Warm blue wool for winter, lightweight white canvas (or whatever) for summer?