Re various battery shapes, it IS possible, but not economically feasible. Virtually all Li-ion batteries used in portable devices, including 1) standard prismatic Li-ion ones with wound 'jelly roll' electrode-separator assemblies stuffed into aluminum cans, 2) stacked-electrode Li-ion types with non-sticky separators, vacuum-packaged in flex pouches or 3) mostly large-area Li-ion 'polymer'(sic!) cells, such as those used in tablets, ultralight laptops and the newest smart phones, are rectangular in shape, with a uniform thickness. Those that are built-in into some curved plastic covers do not efficiently fill the space inside the cover/pack. Making nonrectangular cells is quite possible and it has been done (also, all pacemakers etc have semicircular cells of a different type), but not on a high-speed assembly line; just imagine having to punch out all shapes and sizes of the electrodes, then assemble them in the right order, with the anode always 0.5 mm wider along each edge than the cathode... It would cost several times more than a few bucks a typical cell costs to make, at a significantly lower production speed and yield.
Now, you may ask why do we have to pay $30 or more for a $1 control circuit and 10 cents worth of plastic, and who pockets the difference, but it's a different question... ;-)
And, on a separate note, there are no true polymer batteries on the market; true polymer batteries only work at temperatures higher than 60-80C. All these so-called 'polymer' cells either use microporous polyethylene or polypropylene separators coated with a thin layer of a polymer adhesive (like in a Scotch tape) to bond the electrodes, with the entire stack or jelly roll infused with a liquid electrolyte, or a monomer is added to the liquid electrolyte before the infusion and then polymerized at higher temperature to trap the liquid in something that feels like a Jell-O. Importantly, all of these cells always contain a liquid electrolyte; the gluing is done just to keep the electrodes and separators in close contact without the need for a heavy metal can.