In my experience, they absolutely lived up to it.
The only possible exception is in regard to scratches, skips, etc. Early Sony players were able to deal with scratches just fabulously, but later, cheaper models not so much. I suspect that the error-correction circuitry is relatively expensive, and so was dropped or scaled down for consumer-priced models.
Still, they handle scratches far better than vinyl, and the hot interior of a car far better than cassettes. Also, a CD can be resurfaced for a couple of bucks and returned to like-new condition. How about the scratched LP's?
I think CD's are and were everything I'd ever heard of or hoped they would be. But maybe that's just me. ;-)
They were hyped as being the end-all of recorded sound. While modern music production methods might be mostly to blame, certainly, they are not and have been surpassed by SACD & DVD-A.