Does anyone actually use the teachings of My System that much?

It's one the most famous chess books of all time. For a master not to have read it is almost unheard of. I read it many years ago (twice, actually) and I thought it was quite clever, the way he uses overprotection, artificial support points for knights etc. That was the way I wanted to play chess!

Yet, that was  20 years ago and ever since I personally have seldom used any of the techniques Nimzowitsch uses. I rarely use his favourite openings either. In professional leagues too, it's rare to see many players follow in his footsteps, except for maybe Petrosian and Karpov.  I usually go for a more clear cut style that emphasizes piece mobility. 

So is it the true chess bible, or just a book that you feel you're "supposed" to admire?

Fantastic question.

My System is definitely one of the foundations of hyper-modern Chess theory, but it is far from complete, and really fails to address many subtle complexities of modern play.

I'd personally say read it, play the positions and learn what you can from it, but don't take it as "canon truth".  Recognize that Chess, like any worthwhile sphere of human creative endeavor, continues to change and evolve.  "THE" definitive work on Chess theory has yet to be written, very doubtful any of us will see it in our lifetimes.

That depends on what quantum computers have to say about it, when those machines are fully realized in the next few decades.

Chess may end up being a finite closed system, like Tic Tac Toe... always a draw, or won by white even with perfect play by black.