The speeches may be scripted, but the U.N. General Assembly can sometimes be the only direct window into the regional challenges that command global concern.

On Saturday, world leaders were speaking on behalf of some of the most unstable and unsettling current conflicts. That includes India's fight over the Kashmir region with bitter rival Pakistan, Haiti's domestic crises spilling into a migrant crisis at the U.S.-Mexico border and questions about the Ethiopian government's role in reported starvation deaths in the Tigray region.

Haiti Prime Minister Ariel Henry didn't shy away from addressin...