Rest assured, NASA and SpaceX engineers don't have to show their work either.
Yes they do, at least internally and for regulatory purposes.
Same thing as a Structural Engineer; when i used to design bridges i had to provide heavily detailed calculations that were reviewed for regulatory and safety purposes.
It's even worse in areas that are prone to earthquakes, just preparing the calculation booklet took weeks of time. We actually stopped doing work in California because their regulatory process was so overbearing we couldn't make money off any projects.