The question needs to be clarified before it can be answered.
By mainstream currency, do you mean fiat currency? If you do here's the reason it can't happen:
Fiat currency is established as money by government regulation or law. The term derives from the Latin fiat ("let it become", "it will become") used in the sense of an order or decree. Government fiat is minted and controlled solely by the issuing government.
By mainstream currency, do you mean a regularly used means of exchange used by the masses? If you do then it depends on government regulations and acceptance.
Japan for example is becoming more open to Bitcoin than any other country. The U.S. treats Bitcoin more like a commodity and has stiff laws against making a competing currency. In the U.S. a man named Bernard von NotHaus was found guilty of counterfeiting charges for minting and distributing a form of private money called the Liberty Dollar. There are ways around that problem even in the U.S., during the Great Depression, local governments, businesses and individuals issued currency, known as scrip, to keep commerce flowing when bank closings led to a cash shortage. Scrip is legal but, by law, may not resemble federal bills or be promoted as legal tender of the United States. That's kind of where Bitcoin is now but people have always been hesitant to accept scrip as they would government fiat. It will take some time for wider acceptance to happen because trust must be established first.
You're right, Bitcoin could serve all the functions of money you outline. It could be a medium of exchange, a unit of account, and a store of value. Widespread use as those functions depends on governments regulation of Bitcoin (or lack of), the individuals willingness to accept scrip instead of their local fiat, and bitcoins continued evolution. Right now, today, Bitcoin isn't ready for the job.