I think the truth lies somewhere between "it's just a descriptor, you can't write to it" and "you can specifically design a game to GNS" (I forgo the Big Model so I'll just talk about this from a GNS perspective).
GNS helped people understand the different viewpoints players take towards a game. It helps explain a lot of the conflict that arises among players, and players and GMs, and players, GMs, and the games they are using. This is because the gamist, narrativist, and simulationist approach are somewhat coherent approaches that people can either like or dislike. Really they are like any other deconstruction of a medium - like something that tries to categorize "major types of horror movies and their tropes." It starts out as purely descriptive of gamers' approach to an RPG.
Of course, once you have such a deconstruction, people can choose to start making their games with it in mind - just like horror movies can and often do adhere to the identified tropes there (the couple that has sex gets it first!) Like anything like that, it can be helpful - "Hey, I've written a game that caters a lot to simulationist types, what kinds of things do they tend to like/not like?" Or harmful - "What, did someone write this movie out of the horror movie playbook after reading TVTropes too much? Suck!"
I'm not a big Ron Edwards guy, but his essay System Does Matter helps illustrate that the RPG and its mechanics can and do facilitate certain play styles. Sometimes people claim it doesn't, and that you can do X regardless of the game rules - but that's like saying you can play an immersive character in Monopoly. It may be possible if you've had enough absinthe, but the game itself certainly does not help you and in fact actively harms your attempt at that.
I think more and more RPGs acknowledge GNS/the Big Model in that it helps to clarify their approach. Back in the old days, RPGs tended to think they "had" to be simulationist. In the '80's heyday, many people evaluated games based on whether anything about them "broke realism." (This was before the Internet, where you had to call realism "versimilitude" to get the people who chortle "realism with fireballs? haw haw" to shut up.) People would try to graft on specific little "cinematic bits" or whatnot with limited success. However, with GNS they realized, "Hey, we can do, for example, a fully narrativist game." A lot of the games in the indie scene now are almost completely narrativist often with a strong side of gamist at the moment. It helped them say "Hey - simulation is just one goal, I don't actually have to include it as a supported agenda in my game."
And an understanding of the model helps understand certain conflicts. I don't want to open up an Edition War discussion, but IMO a lot of the concerns previous version players had about D&D 4e is based around it making some changes that move away from supporting simulationist play to supporting gamist play. When you hear people say "4e sucks," it is usually an uneducated way of trying to express something that game theory can help make more nuanced, like "in this edition, the game is advancing a more gamist agenda, making it harder for me to conduct simulation and in fact changing base assumptions among the player base I interact with to be more gamist. I don't prefer that method of play."
Therefore I would argue a lot of games are designed somewhat around the Big Model, in that most game designers have heard of it and it helps refine their understanding that there's players that like sim, drama, or challenge and that their game will appeal/cater to some of those based on how they write it.