Yeah, the best I've done by PC is rounding the edges over.
I'd consider a *light* wetsanding with Meguiar's/Nikken unigrit (2K or 2,500 grit) and then correct the sanding scratches with the PC/4". IMO that approach would be more likely to both reduce the etching while removing the least clearcoat, *BUT* you have to know when to say "enough" with the wetsanding, and I wouldn't do much.
IMO/IME it can be easier to do this sort of thing in a controlled manner with the sandpaper than with a polisher.
FWIW, I have etching on most (all?) of my vehicles that I just live with because I don't want to thin the paint enough to fix it.