By now, you’ve probably heard the yarn about a young and pint-size Mary Jo White challenging a boastful male colleague to a tennis match, riding up to the court on a red motorcycle, and proceeding to beat the braggart. If you haven’t, take a glance at some of the laudatory pieces about President Obama’s decision to nominate White, a veteran prosecutor and corporate lawyer, to head the Securities and Exchange Commission: the story features in more than one of them.

Clearly, White, who was the first woman to serve as the U.S. Attorney for the Southern District of New York, a post in which she earned a reputation as independent and dedicated, is an impressive piece of work. Still, there are two significant objections to having her run the S.E.C., the agency that regulates much of Wall Street.

First, should we really reward people, even women who have broken through the glass ceiling, for exploiting the revolving door between public office and private enrichment?

After leaving the U.S. Attorney’s office, where she prosecuted plenty of mobsters and alleged terrorists but relatively few Wall Street wrongdoers, White joined the law firm of Debevoise & Plimpton and built up a lucrative practice defending, among others, senior Wall Street executives. Her clients included Kenneth Lewis, the former chairman and chief executive of Bank of America, and John Mack, who held the top job at Morgan Stanley. Partly because of worries about going up against high-priced lawyers like White, the federal government has yet to bring criminal charges against a single senior Wall Street figure for the disastrous lending and underwriting practices that led to the financial crisis. While everybody deserves a proper legal defense, even overpaid Wall Street C.E.O.s, it seems a bit peculiar for a President who has repeatedly pledged to crack down on Wall Street wrongdoing to pick as one of his top financial cops a figure who has spent much of the last decade defending senior bankers.

Back to White. One defense of her career path is that government lawyers, after years serving the public at relatively low rates of remuneration, deserve the chance to make some real money in the private sector. If the practice was banned, the government might well have difficulty attracting talented young lawyers. Perhaps. But should the Obama Administration be actively encouraging the revolving door by naming White to such a prestigious position?

One of the lessons of the financial crisis was that regulators at many government agencies, not just the S.E.C., had effectively been captured by Wall Street. With the heads of the agencies more interested in hobnobbing with top bankers than challenging them, the grunts in the enforcement divisions had little encouragement or incentive to try to bring big cases. White sounds like more of a cop than a glad-hander. But we’ll have to take it on trust that she won’t be hamstrung by the fact that, for the past ten years, she and her law firm have been taking hefty retainers from some of the banks she would be in charge of regulating. If she were a Republican and President Bush had nominated her, I think the media reaction would have been rather different.

Another argument, made by my colleague James Surowiecki, among others, is that White’s experience in defending Wall Street bigwigs will inform her work at the S.E.C., making her a more effective regulator. It’s a variant of the old argument for picking a police chief who knows what the crooks are up to, which is what F.D.R. did when he appointed Joseph Kennedy, a notorious Wall Street speculator, to be the first chairman of the S.E.C. In introducing White as his nominee, Obama intimated that he saw in her a similarly formidable character. “You don’t want to mess with Mary Jo,” he said.

That may well be true. But if White actually is the fearless and fearsome slayer of Wall Street wrongdoers that the White House and her old mentor Senator Charles Schumer are building her up to be, then she may well have been appointed to the wrong job. The agency that really needs help in putting Wall Street executives behind bars isn’t the S.E.C., which has, at least, brought civil suits against Bank of America, Goldman Sachs, Citigroup, and other big banks for their actions leading up to the mortgage crisis. (Many critics, myself included, think some of the settlements of these suits went too easy on the banks, but that’s another story.) The federal agency crying out for a big bad financial prosecutor is the Justice Department, which has yet to bring criminal charges against any senior Wall Street figures for anything having to do with the subprime blowup.

As it happened, White’s nomination to the S.E.C. came two days after “Frontline,” the PBS show, put out a new documentary about the lack of prosecutions, entitled “The Untouchables.” Written and produced by Martin Smith, it featured interviews with numerous congressional investigators and whistle-blowers who claimed that the big banks, and the smaller mortgage servicing companies that worked for them, knowingly combined toxic and, often, fraudulently issued home loans into subprime mortgage securities, which they sold to investors. Such stories are now too detailed and numerous to be dismissed. They are coming to light largely because of investigative work done by law firms involved in private suits against the banks. In some cases, the financial-fraud task force at the Justice Department, which has supposedly been beefed up a couple of times since Obama came to office, interviewed the whistle-blowers and dismissed their stories. In others, it didn’t interview them at all.

On the “Frontline” show, Lanny Breuer, the criminal chief at the Department of Justice, defended the decision not to bring any charges against senior Wall Street bankers on the grounds that the government didn’t have enough evidence to prove criminal intent beyond a reasonable doubt. But the former Senator Ted Kaufman, a Democrat, and others interviewed said the real reason for the dearth of action was a lack of determination to go after the big fish.

Any criminal prosecutor will tell you that it’s often a tough call whether to bring a complicated financial-fraud case. Juries tend to get lost in the details. And without a devastating trail of e-mails or wiretaps, it is hard to prove intent. In the aftermath of the financial crisis, both factors played a part in the government’s failure to win a criminal case against two former two hedge-fund managers from Bear Stearns. But even allowing for these mitigating factors, it is startling that, even today, there hasn’t been a single indictment of a senior Wall Street executive—not one. (The D.O.J. has been busy prosecuting insider trading cases, but these don’t have anything to do with the financial crisis.)

With the statute of limitations running down, the Justice Department will have to act soon or never. Earlier this week, the Washington Post reported that Breuer was stepping down. If Obama is serious about holding some senior bankers to account in a criminal court, he needs to replace Breuer with a gung-ho prosecutor who isn’t intimidated by the prospect of going up against the big banks and their defense teams. Somebody like Mary Jo White?

Photograph by Doug Mills/The New York Times/Redux.