Earlier quoted context omitted.
No, there's no reason, as it could have been written in Ada and gotten many of the same safety guarantees as Rust provides.
Given Ada's history in safety critical systems (avionics), it's actually somewhat surprising more didn't use Ada. They could have just adopted the military standard (which is fairly stringent, as I understand it). The military is pretty adverse to losing billion dollar pieces of equipment, so they probably take quite a few precautions.
AFAIU the JSF software is done in C++, there is (or at least used to be) some JSF coding guidelines document on Bjarne Stroustrups web page. Of course, blaming C++ for the JSF boondoggle is unfair, but still, one wonders whether it was wise of the DoD to allow C/C++...