After the crypto exchange FTX filed for bankruptcy last week, Securities and Exchange Commission Chairman Gary Gensler announced that he will crack down on the “wild west” of crypto markets. Meanwhile, Reuters reported that between $1 billion and $2 billion in customer funds held by FTX had disappeared. If U.S. customers lose their shirts, the SEC will bear significant responsibility.

FTX’s bankruptcy was caused by significant losses from previously unknown exposures to volatile crypto assets and the potential misuse of customer funds lent to Alameda Research, an affiliated trading firm. Customers hold more than $16 billion in cash and crypto assets with FTX and can no longer withdraw their funds. They face an uncertain future in bankruptcy that will depend on the extent of the fraud and losses.

It didn’t have to be this way. These crypto assets should have been held, or “custodied,” by regulated banks and broker-dealers, not by unregulated crypto exchanges, but Mr. Gensler and the SEC stood in the way. An independent custodian holds customer assets and controls their movement to ensure their safekeeping and prevent misuse of funds, including those that are due to conflicts of interest, the problem at FTX.

Banks typically custody assets for institutional clients and brokers for retail. The segregation of assets, accounting for them separately from exchange assets, as suggested by Treasury Secretary Janet Yellen in response to the FTX failure, isn’t enough. These assets need to be custodied by banks and brokers, whose regulatory framework can ensure that customers can get back all their funds and not become mere creditors in the exchange’s bankruptcy.

The Journal also reports that FTX suffered a hack of $370 million in customer funds. Banks and broker-dealer custodians can also protect against the risk of theft or loss from hacking better than crypto exchanges, as they have control of the assets and more cybersecurity experience.

The SEC put Americans investing in crypto assets in harm’s way. We and others warned the SEC that their policies might have this effect.

The SEC Staff Accounting Bulletin issued in March required banks and their affiliated broker-dealers that custody crypto assets to include custodied assets on their balance sheets. They weren’t required to do this before. This change would be very costly for banks and affiliated broker-dealers because it would subject them to higher capital and liquidity requirements. As a result, these financial institutions have largely stayed out of the crypto-custody business.

That is a big problem because the largest and most sophisticated custodians in the world are all banks or broker-dealers affiliated with banks. The new SEC accounting rule prevents firms such as State Street and BNY Mellon, which custody trillions in financial assets, from custodying crypto assets.

So why did the SEC implement this rule in the first place? Other financial assets such as equity, derivatives and debt securities aren’t required to be on a custodian’s balance sheet because custodians don’t own these assets and thus aren’t exposed to losses from changes in the value of those assets. Yet the SEC applies special rules to crypto.

According to the SEC, crypto assets have “unique risks and uncertainties,” including risk of theft or loss and concern over the legal treatment of custodied crypto assets in the event of bankruptcy. But the SEC is wrong. Banks and broker-dealers have operational capabilities, regulatory obligations and bankruptcy rules that mitigate these risks. Broker-dealers, unlike crypto exchanges, are also subject to regulations clarifying how to custody crypto assets safely.

If the SEC rescinded this bulletin, banks and affiliated broker-dealers could offer their services to U.S. investors in crypto assets and to crypto exchanges, placing crypto assets in the hands of the safest custodians in the world. Indeed, these banks and broker-dealers had begun to do so before the SEC’s new rule. The value of crypto assets could still fall, but U.S. investors would no longer have to worry about losing their assets because of a crypto exchange gone rogue.

Most of Mr. Gensler’s attention has focused on completely remaking the U.S. capital markets in a way that increases costs for investors, as we have detailed in these pages before. When it comes to crypto, most of his attention has been on asking unregulated exchanges to register voluntarily with the SEC and to provide disclosures for crypto offerings, not on protecting customer assets from unregulated crypto exchanges. While the SEC lacks the power to order unregistered exchanges to provide for independent custody by regulated financial institutions, he shouldn’t have stood in the way of the market adopting this solution. Mr. Gensler should rescind this rule now, and Congress should mandate independent custody of crypto assets by broker-dealers and banks.

It’s too late for the U.S. customers of FTX, but the SEC and Congress can still protect other U.S. investors in crypto assets before another shoe drops.

Mr. Scott is an emeritus professor at Harvard Law School and director of the Committee on Capital Markets Regulation. Mr. Gulliver is the committee’s research director.