I have been using a bulk tape eraser on my CDs since the mid 90s. It makes a difference. I remember back then I had a buddy come over with some duplicate CDs to mine. So we were able to listen to his untreated discs compared to my demagnetized discs and then demagnetize his and listen again. Since then I demagnetize all of my new CDs. The bulk tape eraser was about $20 at Radio Shack back then. Turns out it works.
CDs have a thin layer of Aluminum sputtered onto the polycarbonate disc. Aluminum is paramagnetic. We also figured some of the CD label inks may have metal in them. Perhaps even weak spinning magnetic fields jostle the laser head. Who knows? Demagnetizing CDs works so i just do it.
My brother worked at Sony making CDs then DVDs until they moved it out of the country. He says CDs have an analog component to them. Part of it is that the time domain is mechanical (The spinning disc) but the part I don't understand is why does a clean disc play louder than a dirty, smudged disc.