Michelle Cochran, a Texas certified public accountant, has been ensnared in costly and repeated SEC adjudications for more than six years. Hers is one of two cases, SEC v. Cochran and Axon v. FTC, that the Supreme Court will hear Monday. The question in both cases is whether Americans hauled before agency ALJs can challenge the ALJ’s unconstitutional removal protections in federal district courts before such unconstitutional proceedings take place.

As it stands, these ALJs can’t be removed by any one person and are structurally beholden to the agency that employs them. Put another way, the constitutional system’s separation of powers made it imperative that the judicial power be separated from the executive. These ALJs are accountable to no one—not the president, not the judiciary (which they purport to replace) and least of all the electorate.

These structurally biased in-house courts strip Americans of their constitutional rights to due process and jury trials, shift the burden of proof from the government to the accused, deprive citizens of the protections of the Federal Rules of Evidence and Civil Procedure, and eviscerate meaningful judicial review—all essential conditions for the fair and impartial administration of justice.

Ms. Cochran worked for a difficult boss who disregarded accounting rules and was the real subject of SEC concern. Ms. Cochran had quit her job in 2013 for those reasons. Nonetheless, the SEC included her as an ancillary target of its 2016 charges though no losses or damages were connected to her work.

Blindsided by these charges dating back some six years, and unable to find a lawyer willing to represent her in a forum where the SEC almost always wins, Ms. Cochran defended the action without an attorney before an administrative-law judge who publicly boasted that he had never ruled against the agency. In 2017 the ALJ hit her with a $22,500 fine and a draconian five-year professional suspension.

In 2018, before her decision was final, the Supreme Court ruled in Lucia v. SEC that the SEC’s administrative-law judges hadn’t been constitutionally appointed. That vacated the decision against Ms. Cochran. She was forced to defend herself all over again before a new ALJ. That eight years had passed since the events in dispute hamstrung her ability to mount a defense.

The new SEC judge assigned to her case was still at least doubly insulated from removal by the president—or any one person—which both the Supreme Court held in Free Enterprise Fund v. Public Company Accounting Oversight Board (2010), and as the government argued in Lucia was unconstitutional. The high court also unanimously held in Free Enterprise Fund that federal courts have jurisdiction to decide such structural constitutional claims. So Ms. Cochran, determined to retain her hard-won right to practice as a CPA, must be allowed to sue in federal court to vindicate her right to be tried only once—and in a constitutional tribunal.

Supported by flawed precedents in five U.S. circuit courts of appeals, the SEC was able to have her case dismissed. The federal district judge who ordered dismissal recognized the injustice: “The court is deeply concerned with the fact that plaintiff already has been subjected to extensive proceedings before an ALJ who was not constitutionally appointed. . . . She should not have been put to the stress of the first proceedings, and, if she is correct in her contentions, she again will be put to further proceedings, undoubtedly at considerable expense and stress, before another unconstitutionally appointed administrative law judge.” Ms. Cochran faced another ALJ decision that would eventually be reviewed and vacated—setting her up for a third trial.

This madness isn’t confined to the SEC. Axon Enterprise, Inc., an Arizona maker of police body cameras, was in a similar bind. The FTC sought to block its acquisition of a small competitor on antitrust grounds without any showing of an anticompetitive effect. Axon was willing to divest the company but balked when the FTC demanded that Axon surrender its intellectual property to the now-competitor. Rather than submit to a yearslong administrative trial the FTC was sure to win, Axon sued in district court so that its case might be heard before a constitutional adjudicator. Axon, like Ms. Cochran, was denied relief and also lost on appeal over a powerful dissent.

Ms. Cochran persuaded a majority of the judges on the entire Fifth Circuit that this process makes no sense. Her victory created the circuit split that brought Ms. Cochran and Axon to the Supreme Court.

These challenges have the potential to turn around decades of accretion of judicial power in administrative agencies. Thomas Jefferson wrote that “the most sacred of the duties of a government” is “to do equal and impartial justice to all of its citizens.” An agency that serves as lawmaker, prosecutor, judge and court of appeal makes a mockery of Jefferson’s aspiration.