Polishing machine for headlamps

Hello, the TÜV thinks that the headlight glasses of my car are too “blind”. Therefore I bought for the sake of simplicity and because there was no finer grinding paper than 1200er in the hardware store a refresher set with small pieces 2000er, 3000er and 5000er, polishing paste and sealer (naja). Since polishing takes some time and effort I thought about buying a used, cheap polishing machine, e.g. King Craft KCA 250, for small money. Jetz I have read here and elsewhere that these “simple” DIY and discounter devices are consistently considered unsuitable for polishing, and would like to ask for the technical reason: Why are these devices consistently so unfit and what technical criteria are they, by which one can recognize the basic suitability (speed, power, or … or … or). Do they at least do something for the “polishing” of headlight glasses? Mick