It is necessary to be interested in vibration because it has a major affect on the performance of your pump.
Vibration can cause carbon face chipping and seal face opening.
Drive lugs will wear, and metal bellows seals will fatigue. In some instances the shaft movement can cause the rotating seal components to contact the inside of the stuffing box, or some other stationary object, causing the seal faces to open and allowing solids to penetrate between the lapped faces. Packing is sensitive to radial movement of the shaft. You will not only experience excessive leakage, but excessive sleeve or shaft wear also. Additional flushing will be required to compensate for the heat that will be generated by the high friction packing.