ESSEN, Germany—Thomas Kufen, the mayor of this rust-belt town in western Germany, thinks his city has a bad case of refugee overload.

Since the beginning of the year, some 7,150 refugees have flocked to Essen from other towns, twice as many as the city was allocated for the whole year under Germany’s complex burden-sharing mechanism. This, Mr. Kufen says, is more than it can handle.

So...