Would the clock synchronization procedure have worked if we had fired baseballs from the origin toward the other clocks in the grid as opposed to sending out a flash of light? Argue one way or the other. (We will come back to this question in a subsequent Office Hour question.)
Since the frame is jnertial, a baseball shot from the origin towards the other clocks will continue in a straight line and with the same speed, as would light. Although the speed of the baseballs must be the same, and should be known beforehand.
All the previous answers sum it up well. The baseballs must travel a constant known velocity and must move past each clock. Then yes, baseballs or any such object works. These assumptions are difficult to pull off. Light is more practical.
No. Light is emitted equally in all directions and on the macroscopic scale is continuous. Baseballs are discrete objects and can’t be fired simultaneously in all directions, which is necessary in order to synchronize all clocks.