See how experiences differ!
I polished the black plastic "D" pillars of my OBS Tahoe with M205. Looked great. I let it sit for a few days, planning to strip the TSO if they didn't dissipate. Well, they did dissipate to some extent and the plastic looked terrible. Part of it was a "dried out" look (OK, makes sense but this doesn't happen with my other polishes) and it also had some *VERY* light hazing that was easiest to see under the SunGun. My guess is that 1) the oils and that plastic just weren't compatible, 2) the oils did a bit of concealing (of the hazing), and 3) the hazing came from the "sharp", but very fine, abrasives being a bit too much for that particular plastic.
So a different situation could very easily give totally different results.
My bad experience with ZAIO was on the black plastic part of the '00 A8's sideview mirrors. The mild abrasives scoured up that surface something awful and I had to repolish them (quite a bit) with a different product that I normally wouldn't have considered milder than the ZAIO.
Seems like one of those tricky things where a seemingly sensible approach can sometimes bite you, or NOT as bswombaugh's experiences show. So IMO it's not a right/wrong situation, just a "you never know until you do it" one.