I’m not sure if you know much about noise - but 60dB is not that loud. Normal conversation level.
If you exactly double the volume. You arrive at 63dB. (Every 3dB is a doubling of the level of noise).
It’s been a while since I worked on sound/noise, but I believe if you listened to noise at a level of 80dB for 8 straight hours, after 8 hours you’d become at risk of experiencing damage to your hearing.
I haven’t studied ANC specifically, but if you use a normal set of headphones, and you turn the volume up to drown out the residual background noise as well as enjoy your music. Say took your headphones from 80dB to 83dB after four hours of listening you would start to damage your hearing.
However, if you have noise cancelling headphones, meaning you can cancel the residual noise out at 60dB and then double the volume of noise by turning it up to just 63dB you would be able to enjoy your music or podcast without damaging your hearing.
The problem I noticed when I studied the volume of people’s headphones is that people actually tend to turn their headphones up quite a lot louder than they should. I personally at one point had mine set around 95dB which if I listened to my music at that level for longer than 15 minutes (which I was) I was damaging my hearing.