OK...
Well, I will agree that _each piece_, as you point out, is primarily functional. But I disagree with your approach of breaking it into pieces (the shaft, the enclosure, etc., etc.) They are ultimately all a whole, a clock in a mountain that will last for 10,000 years (and, note, play music -- MUCH of the design is devoted to the music, which is an undeniably aesthetic experience).
The point is, the WHOLE THING is set up for an aesthetic experience and to encourage certain ideas. To see that it's not designed mainly to be "functional" as a clock, just imagine how absurd that conversation would be.
"Hey, we need a better timepiece. Atomic clocks are great, and so are watches, but they keep wearing out. Let's build a big clock in a mountain in Texas so we'll never have to buy another clock again!"
No. It's NOT being designed because we want something to keep time. It's being designed to keep time so that it will communicate ideas and create an aesthetic experience -- intimately tied, yes, to time, just like some of Dali's paintings of clocks (which were not functional at all, of course).
And that is just what art is. How you can say this clock is primarily designed to be functional, I just don't see. It's no more true than saying the ceiling of the Sistine Chapel is mainly there to keep out the rain.