Tseric from Blizzard confirmed today that it is their intention to allow arena battle to become viewable by other players, as per this post in the forums.

This is something we have considered and agree that it would be a cool feature. All that separates us from doing that is a large technical undertaking. It is on the table, but there are other large-scale things we are attending to at the moment.

So, it looks like its coming, it just may take a while.