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).
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.