I have a pet theory that the smart people at the NSA are aware that politicians with 4 year terms aren't effective at long term financial planning. The current debt situation coupled with the last ~30 years of mostly loose monetary policy has set the US up for serious problems if it doesn't come up with another world-changer like the ICE, electric light, or internet. Hence, Bitcoin is a hedge industry could embrace against a failing dollar.
I know the US isn't solely or originally responsible for those, but boy it sure ran the ball a long distance.
As far as the US government is concerned, this primary effect of Bitcoin and other crypto is a weakening of their ability to enforce sanctions and prevent money laundering.
If Bitcoin was a government program, it probably wasn't the US government. I'd guess North Korea, Iran, Russia, etc. One of the countries heavily bothered by US-led sanctions, or at least one that doesn't already have an important ~global currency to disrupt.
It seems to have grown mostly in the English-speaking world to start with, but that doesn't seem like a fatal flaw of my theory.
Tor was created to allow contacting people securely from within restrictive regimes, wasn't it? Doesn't seem like the same thing to me. The US has a history of free speech advocacy, not of encouraging others to be able to spend money freely.
It's also a big government though, it is quite possible that some part would have driven something like Bitcoin for its own reasons. It just doesn't strike me as very likely compared to the alternatives.
Most likely, in my estimation, is still probably it being started by non-government to be clear.
I'm pretty sure the US can already do both, and that neither of those would be easier with a US backed cryptocoin.
Literal American cash dollars (which tend to work everywhere, even anti-American regimes) under the table would be more secure. But then assets in other countries are probably just paid through shell companies in those countries with local currency or something.