In a recent paper C.Calomiris (Columbia) and M. Jaremski (Colgate) argue that deposit insurance can reduce liquidity risk, but also can increase insolvency risk by encouraging reckless behavior.
By investigating state deposit insurance experiments in the United States of the early 20th century, they find the introduction of deposit insurance may have actually increased systemic risk, instead of mitigating it (see https://corpgov.law.harvard.edu/2016/11/11/stealing-deposits-deposit-insurance-risk-taking-and-the-removal-of-market-discipline-in-early-20th-century-banks).
The paper also argues that economic models that attempt to explain the attraction of deposit insurance may be less relevant than political ones.
Corporate Finance Lab 