For weeks, Mexico has been in turmoil over President Andrés Manuel López Obrador’s proposed constitutional amendment for judges to be elected by popular vote. Fifty-five thousand judicial employees went on strike as legislators pushed the law forward; the peso fell, and international banks issued dire warnings about the effect of the proposal on the economy.

Even the U.S. ambassador to Mexico, Ken Salazar, issued an unusual warning. The plan, he said late last month, presented “a major risk to the functioning of Mexico’s democracy.” The president responded by angrily announcing a “pause” of diplomatic relations with the U.S. Embassy. A similar spat ensued with Canada.

But Mr. López Obrador’s successor, President-elect Claudia Sheinbaum, who takes office on Oct. 1, has had a more reasonable response. Although she has consistently supported the scheme, Ms. Sheinbaum instructed Mexico’s new Congress to deliberate more on the plan, rather than fast-tracking it as the president and his allies are urging. Ricardo Monreal, the majority leader in the lower house of Congress, suggested it could be approved as soon as Sept. 8.

Mexico’s leaders should do the right thing and abandon the plan altogether, given the harm it could do to the nation. If adopted, it would politicize the judiciary beyond recognition and render it toothless for checking the abuse of power. It would institutionalize the power that interest groups could exercise over the entire judiciary.

Electing judges could incentivize them to issue decisions to win votes and satisfy political constituencies instead of impartially deciding cases based solely on the facts and the law. A politically captured judiciary incapable of impartially protecting property rights would be a disaster for business confidence and private domestic and foreign investment. More ominously, it could open the door to organized crime’s control of the judiciary and undermine the very foundation of the rule of law in Mexico.

Mr. López Obrador’s constitutional reform proposal calls for nearly all judges, including those who will sit on the Supreme Court, to be elected. Under the current system, candidates for federal judgeships in Mexico must pass a public exam, undergo training and be evaluated by the Federal Judicial Council, an oversight body, which then appoints them. Most nonfederal judges are nominated by state governors and approved by state legislatures; in a few states, candidates are evaluated and appointed as judges by state judicial councils. Supreme Court judges are nominated by the president and approved by the Senate.