Samuel G. Hanson, Andrei Shleifer, Jeremy C. Stein, and Robert W. Vishny write,
the specialness of traditional banks comes from combining stable money creation on the liability side with assets that have relatively safe long-run cash flows but possibly volatile market values and limited liquidity. To make this business model work, banks limit their leverage, rely on deposit insurance, but also hold loans and securities that are relatively safe in the long run even if they are vulnerable to short-term price fluctuations.
…In a cross-section of types of financial intermediaries, intermediaries with stickier liabilities hold less liquid assets. Banks, in particular, appears as having extremely sticky liabilities as well as very illiquid assets…act as a bridge between households who want to put their money in a safe place they do not need to watch, and securities markets where even assets with relatively low fundamental risk can have volatile market prices.
My mantra is that the nonfinancial sector wants to hold riskless, short-term assets and to issue risky, long-term liabilities. The financial sector accommodates by doing the opposite. Government is tempted to back the financial sector with insurance and guarantees, and this in turn can cause the financial sector to become larger and riskier than it would be otherwise.
You can make your statement stronger. It is NECESSARY for government to back the financial sector with insurance and/or guarantees. If banking as it is practiced were not explicitly sanctioned by the State, it would be criminal activity. Bank runs are only possible because the law pretends the same money can be in two pockets at once.
(Yes, this is the extreme Rothbardian position.)
Hold enough risky assets and your risk converge to business cycle risk.
It could also be the case that, by reducing rushes to currency, the improved transactional liquidity of deposit insurance allows for a defaulted business to exchange ownership more quickly. Asset prices approach valuations of the theoretical market. Then you might see a given bank take greater risks that are nevertheless safer than they would be absent deposit insurance. The difference would be in the level of analysis.