Even if it's perfectly centered on a nice blackbody point, if the spectral distribution is spiky, it will still look bad in real-world usage
CIE's R96a (1999) remains stuck in a disagreement between scientists and manufacturers. This means that lights currently specified with a CRI value are advertising an inaccurate measure of their ability to reveal the color of objects.
A very good CRI does not guarantee a very good color reproduction, but a poor CRI guarantees a bad color reproduction.