By reading LaniusShrike's opening post, I developed a theory. Thanks LaniusShrike! I hope a similar theory has not been posted. Some ideas here were also inspired by various forums and posts. Anyway, what if the TLoZ characters were kept TP style because of Sheik? Possibly, as someone posted somewhere, Mr. Sakurai thinks Sheik warrants a spot in SSB because Sheik remains important as an SSB character, not a TLoZ character. But why do the TLoZ characters remain TP style? Why not a new style? Perhaps, because Sheik probably only has a TP design, so all other TLoZ characters were made similarly (to match). What could falsify this theory is the idea that Mr. Sakurai could have asked for a new Sheik design to match Skyward Sword or any style he required. Another perspective I've read is that princess Zelda was kept TP-style because the SS Zelda design did not seem appropriate for a combat game. Maybe the TP designs were deemed the most appealing for SSB4.
Here's another question: why was Sheik not replaced with Impa? Perhaps, Sheik has become too important in SSB itself to warrant a replacement with anyone, even the similar, relevant, and more original Impa. Perhaps Mr. Sakurai would never replace any character with another. Impa as a costume probably would never happen, since, despite the obvious possibilities, Mr. Sakurai avoids using alternate characters as costumes, since he probably feels most characters should not be treated as costumes (palette references, like Peach's Daisy palette, are different). Even removing the "Transform" move which bonded Sheik and Zelda is not enough to switch Sheik with Impa. But, perhaps, removing the bond of "Transform" foreshadows the replacement of Sheik in the next SSB if Impa becomes popular enough. Removing "Transform" could have been to simply give Zelda and Sheik new moves, or because Mr. Sakurai precisely wants to ease the Sheik-Impa switch if Impa becomes more popular by the next SSB. The idea of easing changes from game to game came from a user on the Ganondorf thread. But would Mr. Sakurai ever consider replacing one character with an entirely different one? I do not think so, but I do not know what could happen. Sheik does seem to be in a unique situation as a SSB character.