Islamic State’s self-styled capital is in ruins and its population scattered. Who will rebuild Raqqah?

The crowd was seething with frustration.

“We want to go inside!” one man yelled. “They told us when Raqqah is liberated we can go home.”

Some of the U.S.-backed fighters who drove Islamic State militants from the Syrian city in October tried to reason with him. It’s not safe, they said. Scores...