>>But, there's a big problem here, bitcoin requires electricity and global internet to function well, and these kinds of services probably won't be so stable without working government

False premise.

This e-book by David Friedman (son of Milton Friedman) provides the following:

1. Real world examples of how private enterprise has successfully provided the same services as a government i.e. courts, police, utilities, etc.

2. A precise, logic-based refutation of the idea that anarchy would simply lead to the strongest criminal thugs forming a new government

3. A reduction of many common arguments for the governments existence to absurdity.

It can be found here: http://lectormatic.freeiz.com/machoffreedom/Friedman,_David_-_The_Machinery_of_Freedom.html