Reproducibility is just a side effect of lack of specificity, which is the major difference and the entire point of my critique. Design docs don't tell you enough to actually build the thing you want to build.
Assume you hold the view that a design document provides all the information necessary to construct a piece of software without any further design work.
Construct a software development methodology around that assumption. Now remove that assumption, and think about the practical consequences for a team who doesn't realize that the assumption is incorrect until after they have started implementing a design document.
Imagine what would happen if you hired an architectural firm to draw up some blueprints for a house, and then midway into the construction of the house it turns out that the assumptions made in the blueprints are wildly out of sync with what's possible to build.
It is significantly better for everyone involved if management goes into the process knowing the limitations of design documents and up front design.
For more concrete example of the practical problems see the history of the debate between iterative and big design up front methodologies over the last 30 years.
