Our BA wagon had a few noticeable scratches on the windscreen from the wiper arm scratching the glass when a blade fell apart.
They were not deep, but reasonably visible.
I bought a cheap kit from ebay with a few polishing pads and cerium oxide powder and had a go at polishing out the scratches.
It worked quite well.
I just used a little 1" buffing wheel in a Ryobi cordless drill with a slurry of cerium oxide and went over the main scratches, then used a 2" pad to go over the main scratches as well as a wider area.
The main scratches are gone which I am very happy about.
Where I covered a wider area, it still needs more work to get rid of the very fine scratches that the wiper blades have left over the whole screen, but there is also a big improvement there as well.
It is a slow process, but the results are good for removing fine scratches
After 21 years there are also quite a few tiny little chips that are deeper, and I think they would not be removed without polishing all the glass down to the lowest point of the chips. I think they will be staying unless I try the very fine wet and dry sanding discs that came with the kit, but I do not like the idea of causing further scratches.
If you like working on your car and there are scratches on your windscreen, I would recommend trying this yourself.