Not all digital currencies have the ability to bring economic freedom. The digital fiat currency (USD, EUR or whatever) in a bank account can't do much. In particular, digital currencies that are decentralized, open, peer-to-peer, borderless and voluntary are the ones with the highest chance of giving people a way out of failing economies.
There are two levels in which digital currencies can be adopted. Personal and national.
On a national level, this kind of adoption is highly unlikely because bad economies are usually a result of oppressive and corrupt regimes, which by nature will not accept a free market money, for the loss of control it represents.
Which leaves adoption on a personal level first, to spread out until there are more people who have adopted than those who haven't.
Bitcoin and other open cryptocurrencies offer a way out for people living in countries that have economic instability or oppression. Voluntarily, one can opt out of using collapsing that currencies and adopt Bitcoin instead.
It also offers a long term store of value, to hedge against hyperinflation in places like Venezuela and Zimbabwe. Currency controls and other restrictions on the flow of money can also be avoided by adopting cryptocurrency as it is global by design and censorship-resistant.