It seems to me that the core insight of the Big Model is that it's not a typology of players but a typology of games. Of playstyles. If one accepts that, whether you accept the three presented creative agendas or not, it follows that design can focus less on appeasing players as their types and more on offering distinct flavours of games that people can opt to enjoy or not on their own merits. That is, I am not a narrativist; I am simply a player who likes narrativist games but who might enjoy simulationist and gamist games as well if it's clear which mode I am meant to be in. And if one accepts that, again independent of whether you accept G N and S themselves, it follows that typologies themselves are not as important as finding or articulating distinct ways to play a game (however atomised) and building bespoke systems that reinforce them.
First, you identify the players (which is shorthand for playing styles or playing agendas- no, a person is not a roleplayer nor a narratavist, they are not a ego-tripper nor a gamist, those are merely terms used to describe preferences in play).
Then, you use the typology to create a theory of game design.
...isn't that what I wrote in the OP?
But just as interesting as the creation of the typologies is the later application in RPG theory. Obviously, there is the initial typology, which both acknowledged that this was an unbiased look at the games and preferences of players, while also putting its fingers on the scale ... Don Miller provided the answer in A&E 74, that "players and GMs are influenced in their FRP playing orientation by the particular set of rules that they are exposed to ... [players] may be permanently prejudiced by their first indoctrination to FRP. ..." He proposed that systems should have typologies (he offered two Manichean options; simplicity/complexity, and realtiy/abstraction). Stating that he was in the "creative vanguard," Miller then articulated that the rules could no longer be designed without thought or sophistication, and that "a game's underlying philosophy affects everything that the game's systems do or fail to do" and that designing systems can be aided with theory to serve the interests of particular groups.
We can sub out terms, but the "Big Model" is pretty much previewed right there, down to starting out with the typology (which originated as Dramatist, Gamist, Simulationist (Kim/Kuhner, 1997)) before becoming a base for "designing systems that can be aided with theory to serve the interests of particular groups ..." Unsurprisingly, the Big Model ended up focusing on a single creative agenda, because these critical tools used in the amateur community inevitably privilege one approach over others.
Which is great, but is also a limitation and is why they tend to get pushback and the cycle repeats.
(IMO. YMMV. etc.)