T-Mobile CEO John Legere (R) and Sprint CEO Marcelo Claure pose for pictures on the floor of the New York Stock Exchange, April 30, 2018.

Several years ago, Sprint's largest shareholder, SoftBank, quietly approached two of the nation's top regulators with a question: If Sprint were to merge with T-Mobile, would the government approve it?

The answer was an emphatic no.

"The idea of eliminating a pesky rival may have made sense for Sprint, but not for the American consumer," Bill Baer, the former assistant attorney general for the Justice Department's antitrust division, and Tom Wheeler, the former chairman of the Federal Communications Commission, disclosed last year in an essay warning about the prospect of a T-Mobile-Sprint deal. "We made that clear, and Sprint reluctantly ditched the idea."

Well, fast-forward to this past weekend: Sprint and T-Mobile have disregarded that earlier guidance and announced a merger that they argued would "provide U.S. consumers and businesses with lower prices, better quality, unmatched value, and greater competition." They contend that AT&T and Verizon need a viable player to battle against, and that unless they merge, the wireless industry will become less competitive.

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No matter how much hyperbole Sprint and T-Mobile expend trying to sell the deal, it is hard to see how this merger won't turn into a battle with regulators. The transaction would reduce the number of wireless carriers from four to three and, importantly, eliminate competition from Sprint, which has held prices down across the industry by operating as the lowest-cost carrier. To some analysts and market experts, it is a textbook example of a merger that would normally be blocked.

"It would not surprise me if they can come up with an economist with a model that says this is all unicorns and cupcakes," said Michael Kades, formerly a lawyer at the Federal Trade Commission and now the director of markets and competition policy for Washington Center for Equitable Growth. "But the market concentration is presumptively anticompetitive."

Just look at the share prices of AT&T and Verizon after the deal was announced: They hardly moved. If investors truly believed that a combined T-Mobile-Sprint would be a competitive threat and drive down prices, shares in AT&T and Verizon would have fallen significantly.

T-Mobile and Sprint are going to have to overcome basic math as well. One of the tools regulators use to assess the competitiveness of an industry is a formula called the Herfindahl-Hirschman Index. If the index produces a result of more than 2,500 points, the industry is considered highly concentrated and the government starts poking around. If it determines that a deal would cause the number to jump by more than 200 points, it is considered pre-emptively anticompetitive.

So here are the numbers on Sprint and T-Mobile: If they were allowed to merge, the Herfindahl-Hirschman Index for the wireless industry would go from 2,825 — already over the threshold — to 3,258, a jump of more than 400 points, according to the statistics firm Statista.

Of course, Sprint and T-Mobile are doing everything they can to shape the narrative and suggest that the marketplace is much larger.

"This isn't a case of going from four to three wireless companies — there are now at least seven or eight big competitors in this converging market," John Legere, T-Mobile's chief executive, who would become the combined company's leader, said in a statement. He said that the industry is in a mash-up with cable players like Charter and Comcast that are trying to get into wireless, and that AT&T is now the largest TV provider in the country.

It is true that the wireless and cable industries are likely to continue to transform over the next decade, but it is far from clear how the market will be divided. The efforts by the cable companies to get into the wireless game are nascent and, at least so far, unproved.

For better or worse, regulators generally make their assessments based on the current marketplace; they are not prophets.

Part of T-Mobile-Sprint's argument is that the combined company could rapidly deploy the next generation of wireless technology, known as 5G, and that its progress in that area would force AT&T and Verizon to move faster.

"Only the combined company will have the network capacity required to quickly create a broad and deep 5G nationwide network in the critical first years of the 5G innovation cycle — the years that will determine if American firms lead or follow in the 5G digital economy," the companies said in a statement.

They also suggest, perhaps trying to align themselves with President Trump's jobs agenda, that the merger would create more, not fewer, jobs.

But many analysts are not convinced.

"I don't think that is credible," Craig Moffett, a veteran telecommunications analyst from the firm MoffettNathanson, said of the claim about jobs. "And AT&T and Verizon are going to do 5G anyway."

The argument that a merger would make the United States more competitive with other countries in wireless technology is a long shot. The Department of Justice doesn't usually consider nationalism arguments when considering proposed mergers. And Mr. Kades, of the equitable growth center, pointed out that the government is already investigating AT&T and Verizon over allegations they colluded to make switching carriers more difficult, creating an even greater incentive to keep as many competitors in the market as possible.

Mr. Moffett said he put 50-50 odds on the deal's being approved. "It comes down to whether the D.O.J. decides to use the traditional lens of consumer welfare as measured by consumer prices," he said, "or whether they use an unconventional lens about access to new technologies."

He speculated that Sprint could privately take a different approach with regulators behind closed doors, arguing that it "is a failing firm absent this merger and that there is no real path to sustainability without T-Mobile."

That might generate some sympathy from regulators given the hemorrhaging of cash at Sprint and the additional funds it will need to build out a 5G network. But if history is any guide, it wouldn't help the deal's chances of being approved.

Back in 2011, AT&T tried to buy T-Mobile, and one of the arguments for the deal then was that T-Mobile needed a lifeline. The government blocked the merger.

"T-Mobile has not just survived but thrived," Mr. Moffett said, noting that regulators "are still taking victory laps" for the competition that ensued after it blocked that transaction.

Even if Sprint were to fall into bankruptcy several years from now, it isn't as if it would disappear. It would most likely go through a restructuring and would probably be snatched up by a cable operator, creating even more competition.

Would it be fair for Sprint to have to go it alone? Maybe not. The company is clearly the laggard in the industry and desperately needs to gain scale. But our antitrust laws were not created simply to help struggling companies; they were constructed, ultimately, to benefit customers.

(Disclosure: Comcast is parent of CNBC.)