They're unreadable because CDRs aren't an archive mechanism. They break down rather rapidly. Their shelf life is similar to a floppy disk. After 10 years, the odds of being able to read a CDR that wasn't stored in perfect conditions are pretty low.
Are you sure it would be as quick as 10 years? I have music CDs and mixes easily from the early 2000s that still work. A few years ago I found a Jurassic Park soundtrack that still worked.
My parents have CDs from the 90s that still work.
Would there be a difference in a music CD you bought from a store and one that burned yourself?