Gary Gorton has a new and excellent paper on this question. It is called "Questions and Answers About the Financial Crisis." Here is one excerpt:
Q. Why doesn't the repo market just use Treasury bonds for collateral?
A. A problem with the new banking system is that it depends on collateral to guarantee the safety of the deposits. But, there are many demands for such collateral. Foreign governments and investors have significant demands for U.S. Treasury bonds, U.S. agency bonds, and corporate bonds (about 40 percent is held by foreigners). Treasury and agency bonds are also needed to collateralize derivatives positions. Further, they are needed to use as collateral for clearing and settlement of financial transactions. There are few AAA corporate bonds. Roughly speaking (which is the best that can be done, given the data available), the total amount of possible collateral in U.S. bond markets, minus the amount held by foreigners, is about $16 trillion. The amount used to collateralize derivatives positions (according to ISDA) is about $4 trillion. It is not known how much is needed for clearing and settlement. Repo needs, say, $12 trillion.
…to get a sense of the magnitudes, suppose the repo market was $12 trillion and that repo haircuts rose from zero to an average of 20 percent. Then the banking system would need to come up with $2 trillion, an impossible task.
One bottom line is this: the repo market funds the banks and there isn't enough "safety" to ensure the repo market is always working well. We ended up using synthetic securities, including those backed by mortgages. So every now and then we get a run on our banks. Gorton predicts the crisis was not a one-off event and it could happen again.
One implication of this (my inference, not found in the paper) is that most (all?) major current proposals for banking reform don't get at the real problem. You might wish to go back to "old banking" but according to Gorton that stopped being profitable during the 1980s. There's always an uninsured place to put your money, regulation can't stop that, and such money can find its way back to help fund the banking system, right? The systemic implications of that can prove scary.
I read all the same material that you do about "shrinking the banking system" or "decreasing leverage." This paper makes you realize just how far we are from making those recommendations work.
Gorton's short paper is one of the best essays on the crisis so far. Here are earlier posts on Gary Gorton and the crisis.