I should be able to reasonably expect a level of service and security that includes the possibility that the enemy may have the information above.
So, if YOUR root password were known by your wife, then you must publish it for everyone to see? The enemy only increases in number the easier you make it for them do use your weaknesses.
If we're assuming that the President will die if ever anyone gets a hold of the guard rotation, for example, then maybe we need to rethink that plan. If I secured my company's assets this way, I'd lose my job.
It's naive to think that the president's only protection is that. Think of all the "useless stuff" that we do with day-to-day security, like setting up both WPA2 AND mac filtering. It's always "just in case." The harder you work to "hide" something, the fewer "evil" people will be interested or able to find it, even if your actions raise orders of magnitude more eyebrows. Look at how RSA encryption is still reliable.
Rockets should not be password-only protection. RSA keys seem to be in order, because, again, if they're good enough for GE and Intel, then they're damn-sure good enough for a NUCLEAR WEAPON!
I was going to make a stronger refute, but just really want to help. There's some circular logic if you want the above solution. Adding an RSA key or any key is moot if the government DOES comply to disclose everything impersonal (I noticed you didn't argue against securing individual soldier's privacy, and applaud you for this.) I'll go a step further: Suppose they added iris scans and DNA checks to the launch codes. Then, being transparent, the state is forced to release the names of those imprinted with the correct DNA, suggesting a physical search to coerce that person for codes and bodypart matches.
In our current world's government, a "proper leak" could release that person's location and cause trouble anyway, but in a fully transparent state, the information already out there is dangerously easy to misuse. An enemy does illegal things without any transparency at all; why give them the upper hand if it will not play by your openness game. All that said, I understand that we need more transparency, but obscurity in the government is done mostly for the same reason parents keep sex from kids until they're ready for it --or, if you may, the location of your firearms: self and general protection.