SEOUL—North Korea’s flurry of missile launches has unfolded with a familiar pattern, coming just days apart and reaching for similar goals. The tests grab international attention, boost domestic morale and flash anger at South Korea, Japan and the U.S.

But the spree of weapons tests—six in just three weeks, including one Friday—carry a potential downside for Pyongyang: diminished returns for a provocation the Kim regime has long deployed to coax a diplomatic reaction from the U.S. and its allies.

Its...