The basic argument of the lawsuit is that Google possesses a monopoly over search engines and search advertising, which it maintains by entering agreements to make its search engine the default on many devices. This resembles one of the claims made 20 years ago against Microsoft’s Internet Explorer. Yet the argument rests on a misconception about the creation and operation of network industries, which will condemn this case—and future ones like it—to failure under sensible interpretations of U.S. antitrust laws.

Initially, the big four platforms didn’t resemble monopolies traditionally prohibited under the antitrust laws. As the Justice Department and House Judiciary Committee admit, they are commercial platforms, built from the growth and development of network benefits, not monopolies created by the merger of former competitors solely to avoid competition and increase prices to consumers. John D. Rockefeller built the Standard Oil monopoly in the 1870s by cartelizing competing oil refineries, first in Cleveland, then across the country, eventually gaining a 90% market share in refining. This cartelization generated some efficiencies as smaller, less efficient refineries were closed down, but its principal effect was to reduce competition among refineries and increase their market power against the railroads.

Similarly, J.P. Morgan and Andrew Carnegie succeeded in the cartelization by merger of previously independent and competing steel manufacturers to form U.S. Steel in 1901. The merger created a monopoly initially constituting two-thirds of steel ingot production. Both the oil-refining and steel monopolies were successively eroded over time by increased competition.

The growth of the internet platforms was entirely different. They have developed internally by offering network benefits—the more people and organizations join, the more useful the network is for everyone. All of us benefit, consumers and sellers, when Google expands its search capabilities. Similarly, all connected to the internet benefit when Amazon expands the range of products it sells and ships. That is how the big four gained large market shares. By contrast, there were no similar network benefits from the aggregation of oil refineries or steel mills by single companies.

While the Justice Department acknowledges the benefits from Google’s possession of scale in the operation of its search engines—according to the Justice Department’s complaint, “scale is of critical importance to competition among general search engines for consumers and search advertisers”—the lawsuit nonetheless attacks Google’s scale and the means it used to acquire it, such as revenue-sharing agreements with rival browsers. This internal contradiction—criticizing Google for achieving a scale that helps consumers and sellers—leaves the Justice Department in an awkward position. That is probably why many other state attorneys general, also hostile to Google and the other platforms, haven’t joined the suit.

The complaint doesn’t demand a coherent remedy. The elimination of Microsoft’s similar restrictive agreements 20 years ago had no effect either on the success of Microsoft at the time or its inability today to compete with Google, but this complaint doesn’t even go there. It asks merely for “structural relief as needed,” as well as attorneys’ fees and costs. The Justice Department doesn’t show, in the slightest, a way to enhance consumer and seller benefit beyond the services provided by Google.

Mr. Priest is a law professor at Yale and a director of the Bork Foundation.