I wonder if there's a danger of comparing the real activity of programming with an idealized picture of engineering.

Most time spent by people with engineering degrees and job titles, is involved in things like organizing and arranging things, fitting things together, troubleshooting, documentation, meetings. Doing "hard" quantitative engineering is rare, and a lot of the calculations have been rolled into the CAD software. Unless designs are really critical, it's possible to solve problems by the rule of "when in doubt, make it stout."

Is this OK? I think it's an outgrowth of the rising complexity of products. As the number of pieces rises by O(n), the number of interactions goes as O(n*2), so at some point the dominant effort is managing interactions between pieces, rather than engineering the pieces.