Most requirements are for, say a hi fi amplifier, where you want to amplify 50mV from the microphone or pickup to a high power level say 50W. So this is an amplitude requirement. I have never heard of a requirement for an amplifier that does not change the signal's amplitude but only its phase.
I would say no, because DC is just that. A small DC voltage from a probe may need to be amplified so it can be measured using a meter. But if the DC does not change then there is no point in measuring it. There are a lot of amplifiers that are used where the DC stability is of great importance, so in the above example if the DC level of the output of the amplifier drifted with temperature, reading the meter, one would be unsure if the change of reading was due to the signal changing or was because the amplifier was drifting.
Frank