Lets put it like this; Aatrox's sword is triple-edged for two reasons: Fantasy design (yes, this is a fantasy setting, where visible functionality is sort of thrown out the window. Look at Garen.) and there's a few unique factors you're overlooking about Aatrox's sword.
- The sword is flexible/malleable - it can extend, warp, and weave. Why you didn't bring this up already and point out how non-functional a flexible sword would be is a little surprising to me.
- The sword is completely under his control. Not only does the blade move, it moves to Aatrox's willing - so he can make any given side of his sword cut when he wants to.
And, please, if we're talking functionality, none of Aatrox's swords look remotely functional outside of the above points (they're flexible and he controls them). Justicar Aatrox's is a paddlesword with a dull edge, Mecha Aatrox's is made of some sort of glass-fiber, and Sea Hunter Aatrox's sword has way too many serrations to be a cutting weapon, it's almost more for hooking than anything else.
Also, you say "Function is fabulous", but I've seen some functional stuff that looks boring and uninteresting as all unholy hell. On top of that, it's all subjective. I like Aatrox's sword because it looks vicious and unique from any other Champion's weapons.
One last point;
Unless you're saying that the blade fits Aatrox's theme because he's a worthless champion and so a worthless blade would be his signature, then that makes sense.
If you want to discuss Aatrox's gameplay aspects, do so in the Gameplay forum. Because bringing that up here in Story, Art, & Sound both doesn't fit and also derails your original conversation.