I think I have a better grasp of what you mean, thank you for clarifying. Apologies if I'm still off base at all here.
I think in a lot of ways this is tied somewhat to a slightly more common discussion about what happens when games hit players tables - about house rules and unintended rules readings and so on - and my reply is largely the same to that; that we can not control what the players and readers do with our texts doesn't seem to me to be something worth worrying too much about at the end of the day (Except in wanting to make sure our rules are clear and accessible anyway). It's inevitable that people will read our games and do things with our games that we simply have no way to predict or imagine, and regardless of what design lens, tools or lures we use, they may be missed, misunderstood, misread, re-worked or re interpreted. To some degrees nothing of our intentionality survives past first read/play, such is Death of the Author I suppose. You have no control over what the players ideas or desires are, only in how you communicate your own expectations of their play. A Platonic Session might also be understood as your work luring the players meshing perfectly with their desires and ideas. An impossible reality, but as a hypothetical, its a useful tool.
I'd also say that your platonic session isn't a set-in-stone thing established at the start of your project, I'm sure we've all had the experience of writing a game or a system and realizing the very essence of what we were aiming for wasn't working and had to rework the fundamentals or even scrap it. Understanding what you want people to do with your game in the end is just another part of the design process - The Platonic, or Perfect, session of your game may be very different by the time you finish writing, but there's still a lot of value in understanding it and being aware of it, even if it changes drastically after your first playtest or rewrite or what have you.
I should also maybe specify that my idea of a Platonic Session is strictly a design tool, it's not really useful to anyone after you've put your work out there - Think of it the same way some people write a guiding principle or a mood board. Its intended to keep you on track with what you're trying to make, rather than an attempt to bind players to that specific vision.
For the last part here, I'm worried the idea of a platonic session (the design tool intended to help inform a designer and guide the work process) is getting a little mixed up with the overall advice of providing narrative tools (a player-intended inclusion).. All games that intend to tell stories should have information and education for how those stories work and function, and its my belief that all games, fundamentally, intend to tell stories of some form. I'd also point out many of the games mentioned that have excellent narrative tool inclusion are actually fairly large games in the grand scheme of things - Spire is actually a great example of one, AW too. Blades was mentioned, etc. Smaller games can be good at explaining very focused, very intentional-narrative and guided experiences, but that's only really one form of what I'm talking about.
Also Edit: No worries! It happens, I should wait some time before replying. I have some thoughts about the specific stuff edited in but I think I largely addressed most of the stuff in some way here, at least, I hope so. Some of it doesn't make any sense anymore but I've already wrote a lot of words. To try and address the first part tho - By conscious or not I'm saying all games are ultimately saying something regardless of the designers intent, and being aware of that something is a useful tool, and many games are published without being actively aware of what that something is. If your intention during design is to make a bundle of machetes with which the players hack their own path through a jungle of your own design - that's your Platonic Session right there.