CRI has to do the hard job of describing a spectrum using a single number. It's like looking at the entire menu of a restaurant and having to say how healthy the food there is. (heck, there's probably way better metaphors).
It does! And it seems that CRI is simply not a useful way to characterize LED light sources, as (i assume) it was established when incandescent and other non-semiconductor light sources were the only option.
To expand your metaphor: it's like judging a dish solely on the balance of flavors while not noticing that the restaurants have started changing the smell of the air, the firmness of the seats, the relative humidity and temperature individually.
