There are many reasons for this. FDTD is extremely general in the geometries it can analyze. Furthermore, as problems become electrically large, the FDTD method quickly becomes more efficient in terms of computer time and memory than other methods since there is no matrix to fill and solve. The FDTD method is the most direct solution of Maxwell's equations possible. There is no preselection of modes or solution form.
Boundary conditions are automatically satisfied.
If a physical phenomenon exists, the FDTD method will include it in the solution. While FDTD is based on a solution grid, this grid is fundamentally different than those used by other methods. The FDTD grid is composed of rectangular boxes. Each box edge is an electric field location, and the material for each mesh edge can be specified independently of other edges. A geometry is formed by assigning different materials to different mesh edges.