Would we like to have a linear circuit application to cause low distortion at the output port?
linear circuit application to cause low distortion

You self-answered that.
Distortion is anything that doesn't reflect the intended input/output behaviour. So, for a linear device, distortion is nonlinear behaviour. So yeah, if you call your device linear, it must have low distortion

Is it necessary for a power amplifier to have only low distortion

Depends on what you're doing with that. Sometimes it does, other times you do things afterwards where linearity isn't as important.