It is the Audio CD that has more distortion and lower bandwidth compared to the LP, not the other way around. SACDs and DVD-Audio discs are superior to LPs in those two specs, but not CDs.
CDs are definitely "good enough" fidelity unless you are a golden-eared audiophile (they're certainly good enough for me), and they are certainly better than MP3 files (which are "good enough" for most people). And they are in other ways superior to LPs. But you do have your facts reversed about the bandwidth and distortion of a CD vs. an LP.

The LP has the bandwidth to resolve extremely high sonic and even supersonic frequencies found as overtones on musical instruments such as triangles, frequencies some say we can feel or sense even though we can't hear them (frequencies which CDs cannot resolve at all and which have to be brick-wall filtered out to avoid aliasing them), and there is no inherent distortion in the LP medium (unlike CDs, where the higher the frequency of the original waveform the less the CD reproduction resembles the original).

Follow this link to see just how poorly an audio CD resolves a 10kHz audio signal with its 40.1kHz sample rate compared to SACD's 192kHz sample rate (and DVD-Audio can sample even higher!): http://electronics.howstuffworks.com/question487.htm

The "sharp point" after many plays does slowly wear out the grooves in the LP and that is indeed a superiority of the CD. And the CD has superior dynamic range. But the LP has less distortion and higher bandwidth.