FabFilter

Saturation has oversampling and AA filter which appears to be minimal phase to minimise latency and CPU overhead, would be my guess.

However, when switching ProQ4 to Linearphase mode, AA filter remains minimal phase, so top-end phase response is still not linear.

I think this is an oversight - you often need to switch to Linearphase for parallel processing, and this effectively voids using linearphase mode.

Second thing is, saturation adds a fair amount of noise. Way more than Saturn2 or Volcano3 for example. Enough that if you compress heavily after ProQ4 saturation, you can bring it to audible range easily.