I see what you are saying but what if the input is low, there may not be enough volume on the amp, say I reduce the DAC to 5%, the amp. may run out of volume.Yes that's right. The 'power' level coming out to the speakers will be exactly the same.
There is a widespread misunderstanding between gain and power. Power is only added at the output (last) stage of the amplifier in order to drive the speakers properly.
The rest of the circuit will be providing voltage gain tempered with the attenuation of whatever is used to control the volume, be it a digital chip or a potentiometer.