Yes, the spectral power distribution is smooth for any approximate black body radiator. That low temperature (2700K) incandescent and high temperature (5000K-6500K) daylight have a range of "color temperatures" doesn't negate the smoothness of the distribution. Human chromatic adaptation accounts for this difference automatically very nicely.
I guarantee you it's very straightforward to reproduce color mismatches with 5000K "daylight" fluorescents that have CRI 90 and higher, compared to actual daylight. The CRI is just short of complete utter nonsense. It's very useful in specific comparison contexts, but requires qualification. It's almost like having your kid come up with a report card that says B+ and you think, yeah OK not bad kid! But then realist they got A's in everything except they got a D in history. Oops.
I guarantee you it's very straightforward to reproduce color mismatches with 5000K "daylight" fluorescents that have CRI 90 and higher, compared to actual daylight. The CRI is just short of complete utter nonsense. It's very useful in specific comparison contexts, but requires qualification. It's almost like having your kid come up with a report card that says B+ and you think, yeah OK not bad kid! But then realist they got A's in everything except they got a D in history. Oops.