What happens when there is a flaw in the design? There's another higher level of design on top of that, with a platonic ideal of the design unknown to humans at the top? Turtles all the way down.
Each stakeholder has a different "design" in mind, and until you actually get specific there is no design, there's just a nebulous, incomplete list of requirements. And if you do try to get specific enough to be reproducible--you're writing code.
None of this is to say that design docs are worthless, just that they can never be specific enough to function as the actual reproducible design the way blueprints would. Thinking of them that way is harmful.
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.
I think they were using "design" as akin to the blueprint to the building. I totally agree with them that in that sense, the code is the blueprint, not the building. The execution of the program is the analogy to the actual construction: the builder (computer) takes the blueprint (code) and builds the building (executes the program) based on it. The power of computers is that the "building" (execution) part is essentially free and infinitely reproducible. But the creation of the "blueprint" (code) is still labor intensive.
The right analogy for design artifacts really is to the higher-level vision definition for a project. Engineers don't just show up and start drawing blueprints; one or more people come up with a purpose and concept for a building project, brainstorm approaches, evaluate trade-offs, come to some consensus on the right direction, and only then start working with engineers to start creating and iterating on blueprints. This vision phase is where design docs fit.