“You want these companies to invest and compete,” said Jonathan Chaplin, a telecommunications expert at New Street Research who has argued in recent research reports for a Sprint merger with T-Mobile U.S. “This infrastructure will underlie the entire digital economy, and if it remains weak, compared to Japan and China, then the competitiveness of our economy is at risk.”

This, more or less to a T, sums up the view of Mr. Son and his top SoftBank executives. And while for regulatory reasons they have been extremely careful to not — publicly or privately — advocate for a merger, they have not been shy in warning about what might happen to the United States economy if it continues to fall behind in the race for global digital supremacy.

Those in favor of a Sprint deal have also pointed out that the two giants, AT&T and Verizon Communications, while making their own digital investment bets, have been diversifying by pursuing media deals, like Verizon’s acquisition of Yahoo and AT&T’s purchase of DirectTV.

So, the argument goes, with the two leading players focused on their media ambitions and with T-Mobile U.S. and Sprint not generating enough cash to invest at the needed scale, a Sprint hookup with its slightly larger peer has never been more critical.

Of course, a deal could happen only if Deutsche Telekom, which owns T-Mobile U.S., agreed to merge. Bankers also do not discount the possibility of a cable deal titan like John C. Malone swooping in to buy T-Mobile U.S.

At a bit over $70 billion in combined revenue, a merged company would still trail far behind Verizon and AT&T, which generate about $125 billion and $163 billion in sales respectively.

Yet a larger third operator could immediately increase investments from the current $5 billion (for the two smaller companies combined) as Mr. Son pulls out the stops to make his network the class of the competition, as he has done in Japan.