Nathan:
I think the reason for I can't accept this perfectly is that I'm unable to act on two different things simultaneously. Being true to the feel/my assumptions of the character till then AND wanting to roll high. I could probably accept this for a game where the motivations of actions are not in the focus but AW seems so much more for me. ("I am harder than weird, so I do less weird stuff than hard stuff" is very limited in my opinion.)
I must agree with your second point to a certain degree. This descriptive (or so to say, prescriptive) function has meaning for me, but sadly not too much. The PCs can be casually compared in terms of Cool-ness, Hard-ness, etc., but this is not too much of a bonus. I mean, I can't see too much of a point of it.
I don't get the meaning of the scaling in absolute values. (Does Hard-1 mean I am puny and/or fragile? Is Weird-1 "normal"? Hot-1? Plane Jane or six-pack?) This gets even stronger when I am curious about [Stat]+0 or the difference between two positive values or two negative ones. I can make a Driver with a strong body and Hard-2. Probably he/she was not enough agressive, so he became a bodybuilder to compensate.
The words are appealing, anyway. I guess glancing at your character sheet and seeing words like Cool, Hard, Hot, Sharp, Weird is a fascinating thing which can make your experience better, the game more focused and fun.