The Argentine peso gained ground late last week after a three-day rout that followed President Mauricio Macri’s crushing defeat in the Aug. 11 primary for a second term. But there’s no sugarcoating reality: The Argentine hunger for dollars has shot up alongside the risk of holding peso assets.

At least part of the small recovery may have come about because on Thursday the central bank put a limit on the amount of dollars commercial banks can hold. Swooning trust in the national currency, anemic growth and an unsustainable...