Since it is the authority that decides what is and isn't valid for patent and copyright. Of course, one could argue that state secrets are just a different sort of copyright if we really want to wonder off the beaten track. To the best of my limited knowledge, in the US, only individuals can apply for patents, though they obviously may be bound by contract to turn the legal rights over to their corporation, university, etc... scientists working for the DoD obviously can't patent the 'Obliterator 9000' they just designed for the military. Similiarly you could say that 20-dollar bills and driver's licenses are copyrighted material, Fair Use let's you photocopy them, but not replicate them perfectly or manufacture new ones.

Ultimately, you just can't really apply laws to the issuer of laws in that kind of way, it would be like arresting the king of some country because he failed to bow to himself and their was a law requiring everyone to bow to the king. This kind of hits the old bit about how you can't sue the government without the government's permission. I can't think of any reason - though there may be - that prevents the gov't from having copyrights, it's just it already has criminal law covering those areas of interest - counterfeiting, treason, etc whereas intellectual property rights are dealt with in civil courts. One singer stealing some singer's lyrics is grounds for a lawsuit, one country stealing another countries 'lyrics' is espionage, a major diplomatic incident, and potentially cassus belli

I would say, at least at the federal level, everything they might wish to 'copyright' already falls under some specific criminal law, making the need for a civil lawsuit rather unnecessary, especially since those same laws make it illegal to profit from a criminal act, they can just seize the money made by infringing on their copyright. Everything else is basically void under freedom of information acts and so on. How well this translates to state, country, and municipal I couldn't guess, since they don't print money or try people for treason and espionage. So, at the national level it's basically moot whether they can or can't.