So I don't think "mining gold" is an appropriate analogy.
EDIT: Case in point: how much did it cost for Visa + Bank to increase a credit-card from $500 credit limit to $2000 credit limit? $1500 of credit appeared out of thin air.
The first credit limit increase "from scratch" costs hundreds of billions of dollars in creating a system of legal compliance, accounting, communication, internal and external risk management, executive compensation, regulatory oversight, credit ratings, cybersecurity, salaries of millions of workers, building public trust in the credit system, writing and passing legislation, even Fed responsibility of building and maintaining a fiat currency.
The second credit limit increase once this system exists is essentially free.
To what extent do these costs need to be accounted for in creating an accurately comparable 'per transaction' metric? By replacing much of the logic with 'just math', Bitcoin has the potential for a much higher theoretical efficiency than the current banking system. Whether market penetration will ever reach the current banking systems levels - and function without replicating these same structures - is certainly highly debatable and for many of the above items implausible.
Bitcoin transactions in isolation are also essentially free - it's the maintenance of the system which keeps it secure and trustworthy that is expensive.