The last time he pushed the concept in Washington, the Federal Communications Commission and Justice Department signaled they were against any merger that would reduce the market to three players from four.
The election of President Donald Trump and the appointment of Ajit Pai to run the FCC give Son an opportunity to try again.
But to win their blessing, Son must prove that the benefits of the Obama administration's decision to maintain a four-player market lower prices, competition, unlimited data packages can't last much longer.
Sprint has had to mortgage assets and cut billions of dollars in costs just to stay solvent, and must now compete for new subscribers with profit-draining price cuts and promotions.
While consumers may enjoy Sprint's five-line unlimited plan for a paltry $18 a line, the company hasn't had a profitable year in almost a decade.
"We can ride this capacity race pretty nicely compared to other players," Chief Financial Officer Tarek Robbiati said this month at an investor conference. "In the longer run, is unlimited a sustainable proposition? Probably not."
Under Chief Executive Marcelo Claure, Sprint ended seven straight years of subscriber losses. The introduction of half-off prices and $5 iPhone leasing broke that streak, but it didn't keep the company from falling behind T-Mobile to last place among the top four providers.
The loans have kept Sprint afloat as the Overland Park, Kan.-based company tries to generate cash. The woes have meant deep cuts to network spending and a focus on a lower-cost technology that will put a vast trove of 2.5 gigahertz spectrum to better use.
While Sprint has struggled, T-Mobile has sharpened its image as the underdog challenger to Verizon Communications Inc. and AT&T Inc., further complicating any transaction.
Armed with billions of dollars in breakup-fee money and spectrum courtesy of AT&T following the collapse of their merger in 2011, T-Mobile has been the biggest disruptive force in wireless, offering features like free video streaming, carryover data and low prices.
An an investor conference this month, T-Mobile CFO Braxton Carter agreed that the regulatory environment is now more conducive to mergers in the wireless industry.
But T-Mobile has become the fastest-growing U.S. carrier, and can sustain itself, he noted. If there were a potential deal, Carter said it would require "a very significant breakup fee."
There aren't any current talks between Sprint and T-Mobile they're actually forbidden. SoftBank can't yet talk to T-Mobile's parent company, Deutsche Telekom AG, because of a gag rule related to an auction of U.S. airwave licenses. Sprint and T-Mobile declined to comment for this story.
For Son, the pressure to build scale isn't easing. Sprint is part of Son's famed plan to build a business empire that can endure for centuries.
His best argument may be that Sprint would never be a robust fourth competitor if left alone, and that putting the carrier and T-Mobile together would benefit consumers by bolstering a stronger third competitor to Verizon and AT&T.
Son can point to Japan for evidence. He acquired Vodafone's failing Japanese operation in 2006 and turned it into a well-financed rival that competes against No. 1 NTT DoCoMo Inc. and No. 2 KDDI Corp.
"The smaller carriers could say, 'We have been the disruptors, and together we can continue to disrupt when we have a stronger capital base,'" said Amir Rozwadowski, an analyst at Barclays PLC.
A theoretical Sprint-T-Mobile merger may also be easier for antitrust regulators to swallow than the AT&T-T-Mobile tie-up, which was thwarted by Obama regulators. In that deal, the second-largest carrier (AT&T) sought to take over the fourth-largest (T-Mobile) to become the new No. 1. With Sprint-T-Mobile, the No. 4 and No. 3 would combine to become a bigger No. 3.
Son joined the parade of executives visiting Trump in December before his inauguration. The SoftBank chairman pledged to create 50,000 new jobs and invest $50 billion in the U.S. through a new $100 billion technology fund.
The gesture helped get Son off to a good start with the president and win a more favorable ally than he had within the Obama administration.
Currying favor with the FCC's Pai would be the next challenge. The new commission chairman has said he isn't committed to maintaining a four-player market in wireless. Yet in an interview with Variety, he also said the current wireless market is "highly competitive" to the consumers' benefit.
"As of a few weeks ago, for the first time, every single national carrier in the U.S. is offering a new, unlimited data plan or is expanding its old one," he told Variety. "That is a situation that is great for consumers. And it is also good for companies that are supplying content over those networks."
Mark Wigfield, an FCC spokesman, declined to comment.
To consumers at least, the decisions of Pai's Democratic predecessors look great in retrospect. And they're getting better every day, with no end in sight. T-Mobile just raised its unlimited data ceiling to 30 gigabytes. Verizon reversed course and finally plunged into unlimited data price battle last month, while AT&T followed with a new unlimited offer.
"It's hard to say the regulators weren't right in preserving a four-player market," Barclays' Rozwadowski said.