There are a lot of interesting rabbit holes in this vicinity that we could go down and take us totally off topic. 
Before jumping into one, let me just note that I agree with you that plot-driven fiction can be wonderful and shouldn’t be dismissed as drivel. American literary culture will be healthier when its opinion-shapers stop insisting that the most interesting things about stories are characters.
Snipped for those who aren't interested in epistemology
It can do so, and it can also result in a shallow reductionism. I wouldn’t join you in opposing “rational” to “intuitive”; intuition is a form of reasoning. The real opposite of intuition is analysis – making sense of things by breaking them down to their parts and looking at how the individual bits relate. There are a lot of advantages to analysis, notably a higher potential for objectivity and replicability, and it’s played a core role in the achievements of Western science and philosophy.
But analytical reasoning struggles with gestalt phenomena, systems whose level of complexity or emergent qualities mean that the whole can’t be fully understood from the parts. The attempt to “demystify” these (common, and important) phenomena through analysis can yield some insights but if used alone ultimately misses the forest for the trees. Making sense of complex phenomena requires intuitive reasoning based in pattern recognition. While intuition doesn’t offer the same degree of objectivity as analysis, it can still yield valid reasons for belief and action. (If we try to say that we’ll only accept intuition that can retroactively explain itself in terms of analysis, we’ll ultimately find that we’ve stripped much of our actual thinking of its validity).
Recognizing the patterns in systems/phenomena we can’t master through analysis often requires metaphor. A really good metaphor can be the key that unlocks a complex pattern to our understanding. But that doesn’t necessarily make the metaphor something we can then trade in for a more “rational,” non-metaphorical concept and expect it to do the same work.
Our relationship to stories is complex. We aren’t just makers or even inheritors of narratives, we’re made by them, they shape our thought and behavior at a profound level. Talking about a story as something we as authors are discovering more than creating isn’t necessarily just a “feels-like” optional metaphor that could be rendered literal by sufficiently careful psychological, linguistic, or anthropological analysis. It’s one lens on a reality that is hard to break down analytically: that our stories (including the characters that populate them) are bigger than us.
You may well disagree with every single thing I’ve said above. But I think it’s an approach deserving more consideration than you’ve been offering.
It could, though I’ve yet to see anything like that in person. It could also be the necessary key that helps the writer keep their intuitive grasp on the character. I think I’ve run into that a bunch of times, judging from how people talk about their experience of writing.
I have. I know the frustration of playing with people who’ve lost sight of the fact that it’s collaborative storytelling, and just want to RP their character even when that ruins the fun for everyone else. But I also know that some of the best bits of my own longest-running campaign came when the players RP’d right off the plot rails I had in mind for them, following what their characters would have done, and I had to start improvising in response.
Worth noting that “character integrity” here is still firmly within the territory of metaphors that imply independent existence. “…without forcing you to write traits for the character that you didn’t want to write because they felt wrong to you” would I think be the most literal you could get. But it’s not clear to me that that’s half as illuminating or productive as the metaphor of being true to the character, even if the latter risks mystical baggage.