Solid propellants burn at a surface.
If they are designed to burn through a hole in the middle, they are not. Cigarette burning produces roughly constant propelling force throughout the burn. The hole in the center of a grain can be tailored in shape to affect burn characteristics just about any way the engineer wants. In most boosters the grain fills the container, except for the hole in the center, and a space near the nozzle. Remember, the grain burns at the surface.