Three strikeouts in four at bats would be barely acceptable in baseball. For a policy designed to prevent taxpayer bailouts, it's an undeniable defeat. In the past few weeks, four European bank failures have demonstrated that a signature feature of the postcrisis regulatory regime simply cannot protect the public. There's no need for more evidence: "bail-in debt" doesn't prevent bailouts. It's time to admit this and move to a simpler solution that will work: more common equity.

Bail-in debt was envisioned as an elegant solution to the "too big to fail" problem. When a bank ran into trouble, regulators could trigger a conversion of debt to equity. Bondholders would take the losses. The firm would be recapitalized. Taxpayers would be spared.

The idea, adopted both in the U.S. and Europe following the 2008 financial crisis, has its share of supporters, including JPMorgan Chase CEO James Dimon. "Essentially, too big to fail has been solved," Mr. Dimon insisted in a shareholder letter earlier this year. "Taxpayers will not pay if a bank fails." Wall Street also prefers this debt funding rather than equity because it is better for bank share prices. In theory, taxpayers and stockholders both win.

The problem is that it rarely works this way in real life. On June 1, the Italian government and European Union agreed to bail out Banca Monte dei Paschi di Siena with a €6.6 billion infusion, while protecting some bondholders who should have taken losses. Then on June 24, Italy decided to use public funds to protect bondholders of two more banks, Banca Popolare di Vicenza and Veneto Banca, with up to €17 billion of capital and guarantees. The one recent case in which taxpayers were spared was in Spain, when Banco Popular failed on June 6.

The largest of these four banks was less than one-tenth the size of $2.5 trillion JPMorgan. Think about that: If bail-in debt couldn't protect taxpayers from a midsize bank failure when the global economy is stable, what are the odds it will work if a Wall Street giant runs into trouble when the economy looks shaky? Or how about when several giants are in trouble at the same time, as in 2008? Don't hold your breath.

Why are governments so reluctant to force losses on bondholders? Sometimes they fear financial contagion. The argument holds water in the case of too-big-to-fail banks: If creditors at one large institution face losses, creditors at others may fear the same and try to pull their funding. Once the dominoes start falling, they are very hard to stop. This is why the Federal Reserve and the Treasury Department, with the support of Congress through the Troubled Asset Relief Program, intervened so dramatically to arrest the 2008 crisis.

When systemic risk isn't an issue, governments may worry that bondholders are politically important constituents. In the recent Italian examples, the banks weren't considered too big to fail, but the bondholders were retail investors. Regulators claimed that this was a unique circumstance, but there always seem to be unique circumstances when bailouts are concerned. What will happen if an important pension fund faces losses?

This is one more reminder that only equity can be counted on to protect taxpayers—and it needs to be raised in advance of economic distress. Although capital standards for America's largest banks are higher now than before the last crisis, they are not nearly high enough. The odds of a bailout in the next century are still nearly 70%.

Large banks need to be able to withstand losses of around 20%, according to a 2015 analysis by the Federal Reserve. But they have only about half that amount in equity because regulators have generously assumed bondholders would take losses. Italy demonstrates that this is wishful thinking. Too big to fail is alive and well, and taxpayers are on the hook.

There is bipartisan support for fixing the problem, but it will require forcing large banks to raise much more equity. They won't do it on their own, because their stock prices benefit when the public takes the risk. Indeed, banks are now moving in the wrong direction by increasing their dividends and stock buybacks. As a country, we must decide what's more important: protecting taxpayers or bank investors.

Mr. Kashkari is president of the Federal Reserve Bank of Minneapolis and a participant in the Federal Open Market Committee.

See Neel Kashkari's Op-Ed in the Wall Street Journal.