There isn't much of that in application software engineering. Some domains have it, like ML and DSP, but most of the code written for startups is ad hoc carpentry, plumbing, and masonry, not applied physics.
You can do a lot with carpentry, plumbing, and masonry without really knowing what you're doing - up to a certain scale. But when you start building giant things without rigorous non-tribal reasons for your design choices, you're only ever going to build things that fall down and break a lot.
Too harsh? I think it's hard to find anyone today who thinks software is acceptably robust and reliable by default. Some products/apps/pages work just fine if not stressed too hard. But generally security, bugs, and efficiency are all poor compared to comparable challenges in hard engineering disciplines.
The only reasonable definition of "engineering" that I know of is on the lines of "the art of building stuff". Writing software fits that definition perfectly well, it's just what people call "software engineering" that doesn't.
Can you elucidate about the sea of measurements that you can extract from software? What are the things that can usefully be measured in the current art?
>made after some analytical process rooted in mathematical and physical laws, from a set of defensible alternatives, under economic and ethical constraints
Ok - how can we do analysis of things that are not measured? In the end all the software design I've ever seen comes down to "this is the best we can do honestly" there could be 100 better ways or this way could be horribly flawed, there's no way to figure this out a-priori.
When I went to college I roomed with a bunch of Aerospace engineers. They spent days and weeks doing structural calculations which were underpinned by physical knowledge of the materials that were in the structures. If the actuator lever for the flap was too heavy or not strong enough when it was made of aluminium then it could be made of titanium instead; but they knew. The sums showed them.
I did CS; at the time we thought that formal modelling would do the same for us.. that is beginning to come back with thing like Lamport's work on TLA+ but I think that the last 30 years have shown us how little we know.
Now yes, people built cathedrals in the middle ages, and bridges. Some of those are around as monuments to their craft. But a lot of them aren't, a lot of them fell on people's heads.
Engineering is the selection of technological solutions to social and business problems, made after some analytical process rooted in mathematical and physical laws, from a set of defensible alternatives, under economic and ethical constraints.
Regardless of what our gatekeeping cousins might wish to believe, software engineering fits this definition.
That many people working on software do not behave like engineers does not change the fact that it exists. That there is rarely any legally-enforced guild structure to regulate the membership of the profession does not change the fact that it exists. Civil engineering existed thousands of years before the word engineering was even invented.