In my own line of work, I sometimes teach junior staff how to delineate drainage areas (rainfall subcatchments) in predominantly urban environments. Oftentimes, new staff will get caught up trying to decide something like "does the left side of this 400 foot street drain to the intersection to the north or the south of the street?" in an area that is 100 acres in size. They are usually surprised (and even a little skeptical) if my answer is "it doesn't really matter", until they better understand the purposes of what we are modeling the area for, and better appreciate the limitations of things like the rational method and how peak runoff works.
This is an example of trying to be realistic about the inherent accuracy limitations of the particular form of modeling that we work on. With this comes an understanding of what applications this model will work for, and what applications it will not work for.
I would be interested in learning from others about where in their own work they can be inexact, and where, in contrast, high degrees of precision are required.
I'll leave this thread with a quote that a colleague uses in his email signature, and another that I remember from one of my engineering textbooks:
"all models are wrong, so honest modelers report their uncertainty first and foremost"
"Structural Engineering is the Art of molding materials we do not wholly understand into shapes we cannot precisely analyze, so as to withstand forces we cannot really assess, in such a way that the community at large has no reason to suspect the extent of our ignorance."
Have you considered developing a tornado diagram to show the relative impact of uncertainty on model inputs as a means of training and communication? For those new to tornado diagrams - copying from Wikipedia - Tornado diagrams are useful for deterministic sensitivity analysis – comparing the relative importance of variables. For each variable/uncertainty considered, one needs estimates for what the low, base, and high outcomes would be. The sensitive variable is modeled as having an uncertain value while all other variables are held at baseline values. This allows testing the sensitivity/risk associated with one uncertainty/variable. In this way tornado diagrams can quickly show where uncertainty is important to the final outcome and where it does not matter.
Regarding your quote on structural engineering, I think it's flawed statement but maybe I'm reading it incorrectly. I think dealing with uncertainty in a meaningful way is a defining element of the art of structural engineering. This can be through analysis, design, conservatism or combination of all three. Structural failures do occur but are rare. It's not about ignorance but knowledge, experience, and wisdom.