For balance I should mention my electrodynamics 400-something prof, who, upon being asked about a particular symbol/concept, ended up taking me on a tour of his lab. He had a pretty cool lab.
He was surprised I hadn’t seen the concept before, I told him I skip lots of class, but hadn’t seen it on any tests and such.

Even at Caltech, I ran into cases of students who seemed too willing to use formulas without thinking too carefully about the principles than involved. But the physics professors at both schools seemed pretty consistently motivated to motivate particular analyses or approximations to ground principles. The only exception I remember is a cookbook-ish treatment of frequentist statistics in one section of a mathematical methods of physics course at Caltech.

Incidentally, I’m not sure “informal” is the right word for what you describe as informal understanding. To me “informal” sounds like a category big enough to include silliness like informal arguments from relativity or quantum uncertainty to conclude that we can’t really know anything, or informal arguments from the second law of thermodynamics to conclude that evolution is impossible or that agricultural production must fail much faster than the Sun because terrestrial “low-entropy stocks” are somehow irreplaceably depleted despite the entropy flow from the Sun through Earth and back into cold space. My guess is that you mean a category narrow enough that it excludes such nonsense, perhaps “reasoning from formal principles which is rigorous but which doesn’t happen to require substituting numbers into algebraic formulas”. Examples of what I’m guessing you mean include (i) the classic tethered-balls thought experiment critique of Aristotle’s theory of falling bodies and (ii) (the missing understanding on display in) heavy boots. I don’t know the right term for that, but “informal” seems like the wrong term.

(Wikipedia’s thought experiment entry gives a citation to Galileo’s Discorsi e dimostrazioni matematiche for the tethered-balls critique, but IIRC the basic idea is at least a century older than that.)

I also gave informal understanding tests to my fellow students. There were two responses; the ones that liked the math but not the physics, and the ones that liked neither. Getting physics undergrads to discuss physics outside of homework is, apparently, like pulling teeth.

This article makes me suspect that the problem is that the students are following the examples of the professors, and if you changed the classroom structure to be about learning instead of not-learning, you’d get more students appreciating the material.