The Blockchain method provided by Bitcoin is an alternative. Designed to be distributed, Bitcoin distributes copies of all transaction histories to anyone in need. These people can then participate in the examination of historical and future transactions. That way, it is no longer the only entity with a determinant of the validity of supply and transaction history, but a comprehensive community. Also, joining Bitcoin will make it unproductive - the larger the community, Bitcoin's Blockchain is more secure than malicious attacks such as hacking.
As the first codified currency, Bitcoin had a reputation and value early on. It also prepares what a decentralized currency should look like, and demonstrates that the idea is something that can actually be successful. In a decade, it has become a global experiment.
So Bitcoin can be a main currency of the world economy. But I do not know at what time.