The Romero tiny tenor mentioned above can be seen here:
http://luthier.peperomero.com/?page_id=286 . To me it looks a lot like a boat paddle design but with rounded corners, I like its looks and aren’t surprised at all that the shape works well.
Fat hips or larger lower bout must, I think, allow a greater sound board area. That larger board, in turn, surely allows more sound to be created by the vibrating surface (which is excited the strings to saddle to bridge vibration transmission chain). To my mind the purpose of the lower bout form is to provide both a supporting structural edge for the sound board and a focal shape that directs sound waves within the Ukes sound cavity towards an exit hole.
The upper bout is, as best I can understand it, a second sound reflector. It redirects sound waves from the lower bout, that missed the sound hole, back towards the sound hole and failing their escape then then onwards towards the lower bout for further reflection back toward the sound hole. I hope that isn’t too wordy and makes sense.
The early double bout shape in which they were near equal in size might not be optimal in some respects but logical enough given the constraints of the time. The fat lower bout is more bulky, uses wider material (so more expensive and difficult to make) and produces a slightly more mid range sound. In times past any of those three points might have been an issue but today they are either much less so or not at all.
Of course I would agree that a Uke’s sound volume and quality are not all about shape, it is but one factor amongst many but it is still part of the culmative effect. My current preference is for (readily affordable and do the job nicely) Pineapple shaped laminate Soprano Ukes, but if I could find a large bout (say 7-1/2” and over) more standard shape for similar money then I’d consider buying one.
I really avoid the 'search for the best sound" path of ukuleledom, because no matter where you are, there is always the possibility that there is something out there that sounds better. So you can never arrive at the destination.
I think that logic is too often overlooked or ignored - thank you for reminding me/us of it. OK some items are more clearly worth seeking out, having and using than others; however there does come a point, and earlier than some would think, when it’s best to stop searching for the next better thing and focus more on enjoying and using what you have already got.