Interesting case study: Jennifer Grey, where we can compare a before and after.
Before: everyone knew who she was.
After: nobody would look twice, just another middle of the road broad.
Admittedly, the nose job came at a time when her youthful glow was already well behind her and fading fast, but still: keeping the original schnoz would probably have kept her in the limelight a lot longer.
Verdict:
Before: WHB, WNHPIC*
After: could not pick her out of a lineup
*(would have banged, would not have put in corner)