What benefit of Bitcoin (to governments) outweighs the cost of not being able to control the value of a fiat currency? I've read some books about finance / economics, and one of the things I've read is that governments often like having the ability to control the value of their own fiat currency.

This allows them to do things like wage a currency war, in which (to my understanding) they temporarily devalue the price of their currency in the international market in an effort to destroy or severely weaken the position of foreign corporations that are competing with local corporations.

Having a fiat currency also allows the state to debase its currency, effectively taxing the holders of that currency (citizens, bondholders, or foreign states using it as a reserve currency) in a hidden way.

Those seem like subtantial perks of having a fiat currency.
Using a foreign currency as legal tender can curb inflation and delimit deficit spending. It will also reduce friction for trade with other countries accepting the same currency.

In some cases the stability provided by using a foreign currency outweighs the benefits of controlling your own currency. 
 [Wikipedia: Currency Substitution] lists for example
 ten countries that use the USD exclusively, as well as numerous other countries that do not maintain their own legal tender.