Royce’s paper had more than one diagram in it — 10 in fact. The first looks like the classic “waterfall” which he calls “risky development process” at the end of the paper. Royce does criticize it then follows that with the iterative (at least between “phases”) version to which you refer and that with several other versions with, and without, any iterative indications, but indicating changes to the riskier approach that he feels mitigates that risk though not without cost.

Your short description of the government approach is why I believe the “waterfall” was adopted in such projects: ease of managing multiple vendors through complete specifications as the communication medium with no undocumented “back office” discussions.