I'm personally of the opinion that the Arkentools represent an entire class of magic over one discipline. Wanda hasn't tried anything besides her Decryption power so we don't really know the limits of it. Charlie's super thinkagrams have a flavor of Foolamancy to them. It could be just the extra power but none of the other thinkagrams have shown the ability to project false images. Likewise, the only way he could possibly know about what Hagar is going to pop and when would be with some powerful Lookamancy. http://www.erfworld.com/book-2-archive/?px=%2F2010-03-19.png
All of the Arkenhammer's powers are similar to Real World stage magic. Stagemancy includes all elements so it's powers seem a bit scatter-shot. If he learns a trick, like making half your army disappear and reappear in your garrison, it would be just as game breaking as the others.
The attuners personalities mostly fit this: Wanda being Naughty, Charlie the All-Seeing-Eye, Stanley the out of control diva. Okay, the last one is a bit of a stretch. Stanley is Erfworld's Charlie Sheen.
I'm of the opinion that Charlie's beef with the decrypted archons might be that they are the only ones who actually know where Charlie's city is located. Ultimate Foolamancy could keep it safe from Findamancers and Lookamancers. I think his endgame plan was to build a fleet of archons and launch a simultaneous sneak attack on every side. He would be bolstered by making nearly every natural ally break alliance all at once with archons mopping up. It would be a giant coupe de grace on Erfworld. Having his location revealed puts him in jeopardy.
You know, assuming I'm correct, the last magic class with multiple elements is hippiemancy. 8 Arkentools seems like it would be way too much to juggle story-wise but a fourth was confirmed early.
Of course, I'm also of the opinion the Arkentools might not be tied directly to ANY
magic at all. They would be limited by the imagination/knowledge of the wielder. If Wanda and Stanley switched tools, Wanda would still be able to decrypt and Stanley tame. Replacing one attuner with another would open a new suite of powers.