A 200 watts rms amp is not going to put out 200rms all the time, neither is an 80 going to put out 80 all the time. To go on what you have said would say that listening to music at low levels of volume is underpowering them and causing them damage with the only way to safely run 200wrms speakers is to run them and a constant near 200wrms power level...
No. Running the amp at low levels will not hurt a thing. That is using the amp within its clean undistorted power range. When we say under powering speakers we are saying that we are using an amplifier beyond its clean power range to achieve an unrealistic volume level. There is not enough clean power available to achieve the desired volume level.
A music signal consists more or less of smooth sine waves sending current in an even push pull motion through the wire of the speakers voice coil. Like any current it produces heat. When the power supply stage of the amplifier is pushed beyond its limits it can no longer feed the amplifier with enough current to produce smooth sine wave forms and it clips the tops (and bottoms) off of them making them effectively square. This manifests itself by causing the voice coils to stay at one end of the now flattened wave longer than it would in a smooth curved wave and potentially overheating the voice coils along with everything that is connected.
I doubt you could stand to listen to sound generated in car at a continuous 200 or even 100 watts to be honest.
