I do believe that is the whole point, to find a fine grit as an abrasive, so scratches can be polished out.
When I was a younger Aircraft Mechanic, I use to polish out scratches in the acrylic canopies on the fighters. We had a kit for doing it that started with various grades of SANDPAPER and towards the end of the job we used an abrazive creme, similar to Jif or Cif or whatever it is. We’d also use Brasso metal polish.
The trick is removing the scratch without distorting the surface, so if you happen to put a slight concave in the surface, it will divert the laser slightly.
That was also one of the things we had to watch out for on the fighter canopies, and the reason it took so long to blend out a scratch - no localised rubbing.
There are a number of CD/DVD resurfacing machines out there. I saw one at Guang Hua market recently, I can’t remember the cost, but i think it was 300-400 or something.