The Fundamental Impossibility of Banking

I was just reading Nassim Taleb's claim that

with ... the costs of the 2007-2008 subprime crisis, the banking system seems to have lost more on risk taking (from the failures of quantitative risk management) than every penny banks ever earned taking risks.

And it occurred to me that due to the no arbitrage condition of modern finance, borrowing short at market rates and lending long at market rates while entirely managing risk away is axiomatically an unprofitable business. Since banking is in fact profitable, then it must be that every dollar of profit and every dollar of every bankers salary that is not paid for by reduced rates to depositors or increased rates to borrowers will be paid for by the taxpayers.

There's no free lunch: a safe, free-market bank is impossible.

(Aren't my Saturday nights exciting?)