Probably because copyright is automatic and patents aren't. You have to actively patent an invention to make sure nobody else patents it, but the same risk (someone else copyrighting the government's work) isn't really applicable on the other side.
Theoretically. The US patent system is a mess, from the rubber-stamp examiners in DC to the ridiculous judges in East Texas.
If an unpatented invention is disclosed publically (not through a patent application), then it becomes public domain and nobody can patent it.
Also, the US is no longer "first to invent", but rather "first to file". You could have a claim that you invented it first, but if someone files before you, you are SOL.