What you call "inverter", and what is actually / indeed a differential pair, is one of the main building blocks of amplifiers and operational amplifiers.
I'm no expert on the topic, but that stage is what compares the input signal with the signal fed back from the output.
https://en.wikipedia.org/wiki/Operational_amplifier#Closed_loophttps://en.wikipedia.org/wiki/Differential_amplifier#Long-tailed_pairDouglas Self has a pretty extensive description and explanation in his "Audio Power Amplifier Handbook".
I hope it won't be terribly illegal or harmful to add a few quotes here.
"The input stage of an amplifi er performs the critical duty of subtracting the feedback signal
from the input, to generate the error signal that drives the output. It is almost invariably a
differential transconductance stage; a voltage-difference input results in a current output that is
essentially insensitive to the voltage at the output port."
"Using a single input transistor ( Figure 4.3a ) may seem attractive, where the amplifi er is capacitor-
coupled or has a separate DC servo; it at least promises strict economy. However, any cost
saving would be trivial, and the snag is that this singleton confi guration has no way to cancel
the second harmonics generated in copious quantities by its strongly curved exponential V in / I out
characteristic [1] . The result is shown in Figure 4.2 , curve B, where the distortion is much higher,
though rising at the slower rate of 12 dB/octave."