It’s not mutually exclusive. It’s just a relatively small factor in the equation. If one were to write out the qualities which make a light good, as an actual formula, CRI would have a pretty small coefficient. Like, maybe it accounts for 5% of the total. If a beam is already 90% as good as it could be, adding an extra 5% via a high-CRI emitter is a big improvement. But if the other factors only add up to 30, adding an extra 5 doesn’t help much. That effort is better spent on improving one of the factors with a bigger coefficient.
There’s a similar rule in programming. Unrolling loops can help make a program run faster… but one should never actually do it unless all other optimizations have already been made, like making sure the algorithm is the most efficient one available. Only then does it make sense to break out the finishing touches like loop-unrolling.
Yes, all other things being equal, high CRI will generally look better than low CRI. But the other things are usually not equal.