I can't answer your question -- though it's a fascinating analogy to draw -- but that link has some of the most extraordinary footage, and some of the most amazing information I've ever read. I'd never heard of Galloping Gertie and was unaware that a bridge had ever behaved, and finally disintegrated, in such a manner. Bad news about the dog, though.
I'm not being very original when I say that music resonates with the soul. No, I'm not going all religious on you, for I equate the "soul" with the subconscious mind. It's that elusive "self" that we have so much trouble identifying and knowing. It's just another name for our essence.
Music continues to puzzle me because one generation's music is another generation's noise; and yet some music endures -- and much of that comes from the very genre that you said impacts on you the most: Classical music.
From time to time we hear reports of shopkeepers keeping teens from loitering by playing anything from Bing Crosby to orchestral music. It usually works and the kids stay away. To some extent they may be experiencing something similar to your own reaction, and yet, about the time Gertie was galloping, Crosby was the idol of the Bobby Soxers and their ilk.
Interesting question, Tom. I'll look forward to reading the other answers.
BTW I accidentally clicked on the "Edit" button. Apologies. No edit was offered.