[bigbacaloa]

When we don't have symmetry we don't know what to do and can't compute anything. Fortunately many situations can be modeled as near a symmetric one. We solve the symmetric one and study it's asymmetric perturbations.

The prevalence of symmetry reflects our inability to do anything in its absence.

[psychphysic]

That's one way to consider it.

The truth is there are many ways to skin a cat and we've found quite effective ways to do it.

The real cause of the unreasonable effectiveness of mathematics is humans ability to constantly rephrase tasks within the wheelhouse of our mathematical tools.

Eventually... There's long periods of humans being stuck and then getting unstuck and history compresses that to appear like constant smooth progression.

But you're right, many people have a bizarre view of the world painted by the Schrödinger equation. That the world is made up for snap shots of fixed particle number defined energy states. Really peculiar if you think about it and quite clearly incorrect (we know it doesn't apply to 'collpase' which is really the way the world is experienced by us). And compared to QFT.