Government does not need to create BTC in order to control or gain financial strength, government globally has an advantage to control of the economy, Bitcoin is a digital currency that was developed by Satoshi Nakamoto, Government cannot be against what they built.
Yes, it wouldn't make any sense if governments had created bitcoin as it was created in a decentralized way, totally the opposite of what governments want. You said it very well with your last phrase:
Government cannot be against what they built.
Why would governments create a problem for themselves to solve? It consumes time, money and energy.
Now there is a lot of work to do about crypto currency, they want its implementation, as it's unstoppable, but first they need to create tons of regulations to fit it on their purposes and goals, that is closest as possible to centralization.