Damping may be seen more as a hindrance. Literally speaking, it is a hindrance because it prevents any form of perfect oscillation. Of course, from time to time stopping is actually a very good thing. Take for example a car. Without damping, there would be no suspension in cars. With no suspensions, it would be twice as dangerous to drive in a car than it is today. The handling of the wheels would be extremely difficult, and breaking will be much uneasy.
Of course damping could provide some disadvantages. Damping can cause additional friction losses and heat build up in certain machineries.