I don't see how having a design goal to allow for a key reuse explains the "usually" part of "fastest MACs use AES themselves, usually with the same key as was used to encrypt". What you listed was the list of MACs that, from my experience, are meant to be used with their own key. That's what I asked about - where did you see them used sharing the key with an encryption cycle ?
I'm not sure if we're splitting hairs or just talking past each other, but can we figure out why it is we care about the world "usually" versus "sometimes" or whatever it is you think is the correct modifier? What's the meta-issue here?
