SNAFU, the Goldwater Nichols Act, and a lot of other "Joint/Purple" rules written into law by Congress defy the kind of clear analytical requirements crafting that can be done under the assumptions embedded in your questions.
Welcom to the actual world, where all is not rational.
The aforementioned rules were written with an eye toward:
Interoperability
Cost saving
and
"make sure enough districts get a contract so that we all get re-elected."
The cost saving goal, as you can see, has been a myth since about 1984 (86?) when Goldwater Nichols was written, and not just on this program.
Yet the rules remain.
Before I get all wound up, I'll stop.