I find that there is a consistent sliding scale of what is at stake that is largely controlled by the number of participants in the game:
If you have very few players, say one or two, or at most three, then play is or can be dominated by the personal stakes of the participants. That means play catering specifically to the player's individual aesthetics of play, whatever they are, play driven by individual character arcs and individual character backstory. A small number of players allows play to cater to exploration of character, either individual players discovering who their character is and exploring what it is like to be someone other than themselves, or low melodrama where characters immerse themselves in thespian RP with the goal of creating emotional scenes.
But the more players you have, the less time you can spend on those scenes that really serve only one or a few player's aesthetic goals. If you have 6 or 8 or 12 players, you can't spend a lot of time on low melodrama with deep character exploration because not only would you never get anywhere in the story, but three quarters of the game would be players serving only as an audience to another player's game play. It might be hours before your turn came to participate, and this is really not an ideal situation.
So the more players you have, the more the game is about group stakes, and group stakes are almost always set by the DM and involve some larger plot afoot in the world. The more players you have, the more the game tends to be about combat, because tactical combat is one of the few situations where everyone can and must contribute to the success of the group, and where everyone has meaningful choices to make on a regular basis. Other sorts of challenges, it almost always makes sense for one player or one subset of the group to overcome by themselves, simply because they are better suited to do and the situation is not one were more numbers provide meaningful assistance. Likewise, the more players you have the less time you can spend on individual character stories, and the less immediate impact a particular character's backstory has on play, and the less proactive a particular player can be in deciding what the stakes of play are. Simply put, the more players you have, the more the stakes of play have to be a result of a consensus, and that consensus almost always tends to gravitate toward, "Let's follow the plot." provided the plot is even remotely interesting.
Of course, this can happen with smaller groups as well, either by choice because following the narrative and challenge are the player's preferred aesthetic of play or simply because the group lacks the experience or skills to play in any other way. But with larger groups, it feels very much like the choice of aesthetics is forced on you, both as a GM trying to manage such a large group and a player trying to play cooperatively with others.
Personally, as long as everyone has fun, I don't think it matters what aesthetics of play that a game caters to, but I do think that designers often fail to realize that some aesthetics of play can't really be central to play unless there is a small group involved. So there is a certain snobbery amongst designers who design games for and play test with 3 or fewer players, that their games are more advanced and simply better more mature games than traditional RPGs which evolved out of play by tables that catered to a large numbers of players.
And I've also regularly encountered games where it seemed like the process of play was intended to cater to aesthetics of play that focused on the actions of a single player and a single GM, and it was never at all clear how the game would be played if you had - as is usually the case - more than one player. That is, it was never clear from the text how the describe game could be shared by more than one player. I think the most obvious example of this was the original Vampire: The Masquerade rule book, where all the examples of play were about the internal struggles of a single player exploring the boundary between being human and being a monster, where as in practice basically no group played the game in that way because they played it as a social game with fairly large groups and the game as described couldn't be supported within a large group. In the case of more obscure games where the examples of play all involve solo play, I often wonder if anyone is actually playing the described game, or if the game exists solely in the experience of someone reading the rulebook.