First and foremost, the statues are a gameplay mechanic - the Elegy of Emptiness enables the ability to hold down multiple switches at the same time. While creative and cool looking, it's really no different than having a bunch of boxes to set on switches.
Subordinate to their role as a gameplay element, they provide thematic enrichment for the Ikana Canyon region and the game as a whole.
There is no new transformation mask for the Ikana region. However, the Elegy of Emptiness draws attention back to how the masks work. For each of the three masks, Link is inhabiting the shell of the individuals whose souls are sealed within the masks. While we always knew this, the sight of their empty statue-forms really underscores this point.
More interesting than the transformation statues, in my opinion, is Link's own statue. This relates back to what the Twinmold Moon Child [I don't know what else to call it...] tells Link: "Heh, heh... Thanks... You're nice. Umm... Can I ask... a question? Your true face... What kind of... face is it? I wonder... The face under the mask... Is that... your true face?" The game consistently discusses the disconnect between external appearances and internal character. When Link is wearing masks, it's very obvious that Link is someone different on the inside than he is on the outside. However, the Twinmold Moon Child's assertion that Link is still wearing a mask even when he isn't should give you pause. We're not talking about a literal mask here - unless you want to claim that the whole game is actually like, Tingle wearing a Link mask, and I offer you sincere condolences if you hold that view - but instead a metaphorical mask.
We are left to wonder if Link's changing bodies (from Ocarina of Time, as adult/child link) and constantly wearing masks and pretending to be others has worn down on his sense of personal identity at all. Can you really be true to yourself if you are constantly walking in the shoes of others? Link is much more than he appears - a Hylian kid from Hyrule. He has all sorts of interesting skills and powers that are not apparent to Termina's population. The entire game teaches us not to rely on appearances - whether it is Kaepora Gaebora telling us to jump onto invisible platforms, or the Gibdo in the basement of the music house being Pamela's father, or Kafei being trapped in the body of a child who is further disguised under a mask.
The Elegy of Emptiness lays bare what the game has been hinting at all along. Without Link to animate the masks he has collected, we seem them for what they really are - empty shells. But to our horror, Link's own appearance is also a mask of sorts. Without you, the player, to animate your in-game avatar, Link, he can't do anything. He's a shell that can only come to life when we choose to play the game. When it comes down to it, the game is not as concerned with Link's self-reflection and self-awareness, but our own. Are you who you say you are, or do you put on masks?
Also they look creepy.
