I don't think the government's goal in improving memory safety is because of Rust or any other particular technology. The government buys technology from wherever, and until recently they never really cared where they got it from. If they need a USB Emulator, they buy the same Chinese Gotek from Ebay that you or I buy, and they get the same "Driver CD" full of buggy, broken English software, written by one person for…
Just like in every other kind of engineering, for software capability pulls the requirements. The only reason everybody is complaining about lack of memory safety now is because there are alternatives for every use case. Before Rust existed, it was seen as an inevitable issue that one must work with, not as a problem to solve.
There were many memory safe languages before Rust, Java and C# evangelized this a lot, though at that time the accent was on memory leaks not on safety. Rust offers an alternative for low level programming and might be faster in soem scenarios then managed languages.