Bitcoin does not only do transactions. It has a smart contract language which allows more and more types of smart contracts all the time. (Yes, Bitcoin is not static as many people think).
The old system is not at all efficient for transactions. Vendors hate credit cards for a reason. Visa alone made 20 Billion Dollars in revenue last year for a reason.
Bitcoin can scale infinitely via the Lightning Network.
Visa is "inefficient" because they supply many many more services than simply transacting. Dispute resolution, fraud detection, customer service, card issuing, and on and on. You know, all of this stuff we'll have to build from scratch for Bitcoin to become even remotely viable as a currency. There's no reason to believe that Bitcoin can make these services any more efficient.
This "service" has pros and cons. It is one reason why vendors hate credit cards. You never know when you can be sure that the payment really was done. Or if it will suddenly disappear again.
Fraud detection:
One reason why fraud detection is needed is that the whole system of "whoever has the number can pull money" is insane.
Dispute resolution is trivial with a 2-of-3 multisig. The customer locks up funds until service has been provided and then in the ideal case the customer and merchant agree and pay the merchant. If there's a dispute, the dispute resolver can forcibly send funds with the cooperation of either party.
> Bitcoin can scale infinitely via the Lightning Network
No it can't . It barely scales to the orbit of Pluto (~5.7 light hours from the sun). You
can not use it to send Bitcoin from one random point in the Oort cloud to another.
> The bits of the old financial system which duplicate bitcoin (doing simply electronic transactions) are very efficient.
Its all very efficient until Mastercard and Visa decide that your line of business should not be allowed to receive money and they blacklist you and your descendants from the financial system forever.
I see no reason all the other stuff wouldn't still be around in a world where bitcoin replaced the dollar.
Also, there is no way bitcoin can come close to scaling to even a tiny fraction of the transactions which happen every day.