Bitcoin will reduce various statism by defunding it - It's not magic, it's just that without a money printer to pay for the state, you get a smaller state, just by virtue of the real tax intake going down.
As for what happens afterwards it's hard to predict, but I see only good things coming of people being able to keep their wealth instead of getting it debased.
@Saifedean Ammous took a stab at predicting what a Bitcoin standard society would look like: He guessed it would resemble The Belle Epoque, e.g. a extended period of peace and prosperity and a renaissance of science and the arts. The Belle Epoque not coincidentally took place on the classical gold standard.
Another post-Bitcoin hypothesis comes from the book *The Sovereign Individual: Mastering the Transition to the Information Age.* The books authors predicted that we would get a gradual shift to competitive minarchist government with the spread of digital technologies. This would culminate in some people becoming legally sovereign, that is acquiring something similar to diplomatic immunity.
Notably this book actually predates Bitcoin, it was published in 1999.
