But better than nothing, surely. I also highly agree it would be counterproductive, though, much like relying on BIFTs and Inspiration to run 5e in a narrative fashion.
Ah, problem solved. CR isn't a narrative game. It's a trad game. 5e does that pretty well, again, though, with little to no help from BIFTs. It does this well precisely because the GM is placed in the privileged seat for all fiction generation and most mechanics revolve around "the GM decides what happens." This gives the GM much leeway to have a very heavy, story-intensive game. That's not what a narrative game is, though, at least in every other corner of discussion that's not solely about 5e -- 5e doesn't even recognize the concept space of a narrative game. So, yeah, this clearly exposes the root of the disagreement.