My wife's new Decathalon bike made the most awful screeching noise when the brake was applied. It wasn't getting better and put her off cycling. We returned it to the store and they did take a look, tried to centre the caliper etc, everything I'd already tried. Because it didn't make the noise when on a stand it was declared fixed. The first ride showed that it wasn't!
On our next visit we saw another chap and he said the pads needed to bed in and the discs get polished from use.
By this time the bike had been ridden for about 300 miles.
I'm not sure if it is a permanent fix but I ended up removing the pads (held in magnetically) lightly sanding the surface and applying a smear of copper grease to the back of the pad. Has it cured it? Not entirely, she can still get it to occasionally shriek but heaps better.
Did the light rubbing down, the copper grease fix it or did they eventually wear in? I don't know.
All I can say is rim brakes are so much simpler.