It's interesting that you name AW as one of the games without platonic sessions - I actually built a lot of this idea from studying it in part and, in the abandoned longer write up I did of this a while ago used it as a prime example of a game that has a pretty solid "intended experience" (a flawed term, as it implies some kind of imposed thing) in spite of its relatively generalized nature. Not every story told with AW will look similar, but they are, by necessity of the games ruleset, told in similar ways.
But I digress - even the most general game has, in my mind, a platonic session, consciously or not, a designer is trying to make something for a particular purpose, to fill a need they see missing or to contribute to a particular ongoing dialogue. When you say you're building games that provide tools for players to do interesting things, the particulars of those interesting things are what make up the fundamental grounding of your platonic session (and the needed guidelines for narrative tools). Some of the comments I made in the thread above this speak on this a little - while it's absolutely possible to limit player (and designer, and GM) creativity with bad narrative design or poor educational frameworks, well made ones are liberating and further allow those wonderful interesting things we're all trying to enable. The goal of the tools I'm proposing and talking about aren't necessarily about telling a particular story, or even a particular type of story, rather it's about informing a reader what stories they can tell with your games they perhaps couldn't with another game - or how the storys they tell in your game would differ from another, similar game.
But, of course, I have to admit I have a personal bias for more focused experiences, so perhaps its some of that creeping in - either way, great points. I agree at the very least that the approach to narrative tools and education must be very different depending on the intent of your design and goals of your game.