That seems to be what John Cochrane is advocating.
In the 19th century, private banks issued currency. A few crises later, we stopped that and gave the federal government a monopoly on currency issue. Now that short-term debt is our money, we should treat it the same way, and for exactly the same reasons.
Read the whole thing. He argues against the conventional approach to financial regulation, which is to allow banks to issue risk-free liabilities with an explicit or implicit government guarantee and try to regulate their risk-taking on the asset side.
While I agree with those who favor a financial system with more equity and less debt, I would prefer a different approach to getting from here to there. I would like to phase out the subsidies to debt finance. These subsidies include deposit insurance, too-big-to-fail, and the favorable tax treatment of debt. All of these ideas are fairly drastic relative to current policy, but they are less drastic than outlawing outright the contracts that create short-term debt.
Consider this recent paper by Harry DeAngelo and Rene M. Stulz.
Debt and equity are not equally attractive sources of bank capital. Debt has a strict advantage because it has the informational insensitivity property – immediacy, safety, and ease of valuation – desired by those seeking liquidity. High bank leverage is accordingly optimal when the MM model is modified to include a price premium to induce (socially valuable) liquidity production.
Or, in my terms, the nonfinancial sector wants to issue risky liabilities and hold safe assets, and the financial sector accommodates this by doing the reverse.
Another recent essay, Taming the Megabanks, comes from James Pethokoukis.