The problem with too big to fail banks is NOT THAT they might fail. The problem is the SPEED with which they fail.
Put another way, if a bank or indeed any other type of firm, GRADUALLY contracts to nothing over a period of a year or two, there is little dislocation: competitors can pick up the business that would have gone to the failed institution.
And the REASON FOR the speed at which banks collapse stems directly from the fundamental nature of fractional reserve. Reasons are thus.
A bank is an entity which makes an essentially fraudulent promise, as follows. 1, it accepts money from its creditors (depositors and bondholders), 2, it promises to return to creditors exactly the sum originally lodged (maybe plus interest and maybe less bank charges), and 3, it then invests or lends on the money lodged in a manner that is not 100% safe. I.e. the value of the loans and investments sometimes falls to level that is less than what the creditors are owed: the bank is technically insolvent.
Technical insolvency doesn’t matter if the situation can be rectified. But if the market gets the impression it cannot, then a bank run starts. And the bank fails within 24 or 48 hours.
In contrast to that and under full reserve, creditors are not owed a specific sum of money. In effect they are shareholders. That means that if a significant number of “shareholders” want out, all that happens is that the value of the shares fall.
And a falling share price does not mean bankruptcy for a bank or any other type of business. But it DOES MEAN the likelihood of a takeover. And that solves the problem – assuming the firm doing the takeover knows what it’s doing. And if it doesn’t, then that firm in turn gets taken over.