For Japanese billionaire Masayoshi Son, a U.S. judge’s recent decision to approve a merger between Sprint Corp. and rival T-Mobile US Inc. is long-awaited payback on his $22 billion investment. But it is far from the triumph the maverick investor was seeking when he announced he was taking control of Sprint in 2012.

At that time, the SoftBank Group Corp. boss was running Japan’s third-ranked mobile-phone company. Combined with Sprint, he gleefully told the audience at a Tokyo press conference, SoftBank was the No. 3 mobile...