TLDR I really liked this bridge and Philip has already covered the relevant practical and historical details below. I was fortunate that he offered to be my guide over a weekend to eastern Switzerland (and bits of Germany and Liechtenstein too) and can say I am in full agreement with all his points. So the best I can offer is my own journey from finding this bridge ugly and boring to thinking it should be inscribed as a masterpiece of human creative genius.

What makes something beautiful?

After a couple of decades of thinking about it, I’m pretty comfortable knowing that there isn’t really such a thing as objective beauty, rather we regularly arrive at things we can agree on as being pleasing mostly based on habit and convention. 

This is something I have been thinking about a lot since my visit to the Salgina bridge. I remember as a 16 year old first seeing pictures in a library book of this bridge and others by Robert Maillart, and being somewhat aghast (in the way only a teenager could be) that something so boring was being treated as something beautiful.
But it stuck with me, would I ever really be able to understand what was beautiful about it?

If you had caught me in my 20s I could’ve recited some sort of academic argument for this bridge being important or attractive, but I wouldn’t have believed it. I would merely just be repeating what I had read in an attempt to seem knowledgeable. And if I was being honest there was a big nag in the back of my mind that it was actually really ugly, and it was just what some academics had deemed important and had therefore persuaded themselves these tonnes of reinforced concrete were somehow graceful.

This basically continued for years, but gradually I got to understand my own tastes, rather than adopting those of learned people. Walking around various towns, cities and world heritage sites I just began to notice things I found beautiful, I couldn’t necessarily understand or rationalise it but I could recognise it. 

Then one day I was on my weekly trip to see my parents. Just as the final hills of the English South Downs make way to the sea, the A3 road stabs through a man made clearing. I had been through this stretch of road hundreds, nay thousands of times, and finally I had noticed that the bridge above it was very obviously a version of the Salgina Bridge, and it was very definitely beautiful.
Suddenly and miraculously this hitherto unremarkable bit of infrastructure on a southern English motorway was suddenly something I found to be rather handsome.

Skip forward to November 2022 and I was standing with Philip on an overgrown and somewhat precarious viewpoint, and I got to properly see the original. It was even more beautiful than I had anticipated, very definitely an improvement on the ersatz version I drive under 4 times a week and understandably a work of genius.

What makes it particularly alluring?
Well I’m still not really sure I know and I certainly don't think I can describe, nor fully understand it. For all my desires I am not an architectural critic, I just like visiting interesting structures.

Here I can certainly identify that the sweeping parabola is very pleasing, the deck holding the road almost delicate and slender, and up close you can see the wood grain left by the forms used to pour the raw concrete (béton brut). Additionally the lovely hike in the late autumn sun with a friend certainly helped put me in a good mood.

Some combination of these, with the knowledge of just how influential and important the structure is made me a little giddy, evoking that same glow I got leaving the Scrovegni chapel or the Kokerei at Zollverein.
Has this given me a full understanding of why I like it? No.
Do I think it should be inscribed on the World Heritage list on Criteria I as a work of human ceative genius? Certainly.

It has been about 5 months since I visited, and I have driven under my local copy at the bottom of the A3 about 50 times, and each time sparks a little bit of joy for me. 

So this is perhaps a main benefit for me personally.
Through spending time developing an interest in art and architecture and travelling around trying to see outstanding examples, it seems that my everyday life can be improved, even if it is just for 20 seconds every week as I drive under some concrete.