Setting plans in stone was the entire Waterfall Methodology where contracts had requirements and milestones locked in and any deviation meant heavy penalties.
This has been so endlessly repeated without thought that people assume it is a fact when the Truth is far from it.
Excerpts from wikipedia - https://en.wikipedia.org/wiki/Waterfall_model ;
* In 1983 the paper was republished with a foreword by Benington explaining that the phases were on purpose organised according to the specialisation of tasks, and pointing out that the process was not in fact performed in a strict top-down fashion, but depended on a prototype.
* Royce's five additional steps (which included writing complete documentation at various stages of development) never took mainstream hold, but his diagram of what he considered a flawed process became the starting point when describing a "waterfall" approach.
* In 1985, the United States Department of Defense captured this approach in DOD-STD-2167A[citation needed], their standards for working with software development contractors, which stated that "the contractor shall implement a software development cycle that includes the following six phases: Software Requirement Analysis, Preliminary Design, Detailed Design, Coding and Unit Testing, Integration, and Testing.
The "Waterfall" is what is imagined as a "Ideal and Rational" process (see D.L.Parnas' paper A Rational Design Process: How and Why to Fake it for motivation - https://ieeexplore.ieee.org/document/6312940). The stages in the model and the issues to be considered in each stage are what is important NOT their order. In practice it was always a iterative spiral model described by Barry Boehm - https://en.wikipedia.org/wiki/Spiral_model
FYI, D.L.Parnas and Barry Boehm defined the field of Software Engineering. Almost all Govt./DoD standards are based on their research and writings.
Royce's five additional steps (which included writing complete documentation at various stages of development) never took mainstream hold, but his diagram of what he considered a flawed process became the starting point when describing a "waterfall" approach.
"Waterfall" specifies the What while "Spiral and Iterative" specify the How.