After looking at several of the weirdnesses of the Master Sword, a couple can be explained as being Japanese influence. For example, katanas have relatively short blades for a two handed weapon, so the Japanese designers may think the longer grip looks right.* Additionally, the katana’s tsuba (guard) is usually a round or oval disk, so perhaps the Japanese designer thought having a round interface to the hand would makes sense. However, katana guards are VERY light–they don’t alter the mass of the sword much–and their grips have rectangular or oval cross sections for edge alignment. Lastly, the blade could also be influence by katanas, because the katana has a fairly simple wedge shaped cross section with a thick back edge. If the designer imagined a two edged sword as being basically the same as two katana blades pushed together back to back, you would end up with the thick, bulky cross section that the Master Sword has.
The grip wrapping is also somewhat reminiscent of the wrappings around a katana’s grip, however, similar grip wrappings can show up on European swords, so that’s really neither here nor there.
* It should be noted, that katanas do not have pommels. They do not need them to balance the weapon when the grip is so long compared to the length of the blade.