Analogies are useful but don't get carried away, especially when talking about something as broad as "the government" (as if it were one singular thing). The fact that a BLM federal officer lost his firearm doesn't instantly mean that all of our Tomahawk cruise missiles are next to be stolen.
The closest thing to the proposed encryption backdoor is the clipper chip proposal of the 90s, and that did have severe vulnerabilities that the authors completely overlooked.
And I'd recommend you watch John Oliver's segment about nuclear launch codes to recalibrate your trust in those officials. We've come scarily close to Armageddon multiple times over the last few decades, which was prevented only by sheer dumb luck. Just because it's the scariest thing known to man doesn't mean the people responsible for it aren't incompetent.
The fact that a BLM officer lost his firearm doesn't instantly mean that all the cruise missiles are next, but yes, the fact that the USG is unable to maintain sensitive records of twenty million cleared personnel does say something about their ability to keep secret information safe.
http://gizmodo.com/for-20-years-the-nuclear-launch-code-at-u...
No thanks.