More Words, Deeper Hole

The problem with banking wasn't really size it was interconnectedness, a large bank is definitely too interconnected to be allowed to fail, however a fairly small bank can be as well and you might not realise it. In 1933 the USA had a devastating series of bank runs wiping out about 40% of the sector, almost all smaller banks, triggered by the failure of Bank of the United States which was only the 14th largest bank. The problem is a large proportion of a banks liquid assets are liabilities of other banks. One bank failing and its assets being suspended pending liquidation puts a bunch of other banks in difficulty potentially causing further failures. The danger of this kind of chain reaction is the reason for staging rescues and dealing with a problem very quickly. There is also the point that rescuing banks is usually profitable as it tends to be a liquidity problem rather than solvency. Outside finance neither really applies.