The CMoy can affect the sound, which is a hazard if you're a purist and fun if you're not. It's biggest win is being a fun and accessible (cheap and simple) entry into electronics. A good audio circuit should have low output resistance. Granted you can get that with a CMoy, but the popular/expensive models don't meet that criteria.
https://nwavguy.blogspot.com/2011/08/op-amps-myths-facts.htm...
https://nwavguy.blogspot.com/2011/05/cmoy-ebay-headphone-amp...