You can, you just can't document it. You can have an entirely character driven story in with a GM that utterly owns the setting, but the problem is you can't document it and communicate it to another GM. So it can never show up in a module the way it plays out in play, because you're dealing with just too many branching paths. You can if you have an intelligent GM have infinitely many branching paths.
We obviously fundamentally mean two different things by 'character driven'. That is, 'branching paths' is a description of a game where the the SETTING (location), that is the 'paths' and how they 'branch' is what is shaping play. I can go left, or right, and the story will then proceed, telling me about what I find in that direction. Sure, I can take those choices based on some aspect of my character's personality or 'dramatic needs', but that decision can only address control of what part of the setting we address, I would be overlaying my character stuff ON TOP OF that. Thus you see setting -> character, or probably setting -> situation -> character.
I'm assuming that 'infinite branching paths' is some way of trying to state how to get around that. In other words if the player has INFINITE CHOICE then they can address anything they want (IE some aspect of their character) as they can access any appropriate type of situation. I don't see how that describes a game that involves any meaningful prep at all. The only situation where there are limitless paths open is, well, maybe not a total blank slate as there can be limitless open paths and still some closed options, but one with very minimal setting/situation. This is exactly a way of describing the play of games like Dungeon World!
Now, the real impossible thing to do is to have totally character driven stories with more than one player and no coordination between the players. I learned that lesson the hard way. I ran several games where the players each started playing out their story and they didn't metagame and as a result there was never a party, just different characters living their separate lives. I even ran a game for my younger brother and his friends where after a few hours the two groups had allied with different rival organizations, one a group of slavers that kidnapped the love interest of a player in the other group. I never got a chance to play that out but it basically had become two different campaigns from either side of the fence of choices.
Well, I can't speak to your experience. I can tell you I've played in 2 different games in the last year run by
@Manbearcat where exactly this sort of thing happened. Both of them generally had 4 players (I think we got up to 5 once in the BitD game). BitD kind of decrees that you are all a 'crew', although I imagine crews COULD split, the rules would need a bit of extrapolation. Still, it didn't happen in our game. Sometimes we had somewhat different agendas, but the crew had a shared history, resources, and some common goals. At one point we got close to possibly a split, but it never happened. Other BitD games don't typically suffer from that either. I've also never seen it happen in a Dungeon World game, nor in our Torch Bearer 2 game. Generally players don't have a lot of incentives to do that. However, I'm not sure why it would be a problem if it did happen.
But there is no way to record and transmit how to do that in an "adventure". I'm not even particularly happy with the typical attempts to record that through a sand box, because even if you don't have a linear story in mind you still need to have the current state of the NPC's motivations and at least a couple of their future "moves" so that you know what the fronts are trying to do and how that will intersect and interact with the motivations of the PCs.
I agree with you thoroughly, you cannot easily write adventures for most narrative games. Torchbearer 2 is a bit of an exception, there are adventures for that. However, its situation are generally very open-ended and not super large elaborate long-running kinds of things. I think the most elaborate TB2 adventure might have 12 obstacles, and require several pages to write up, not exactly TSR Module territory!
None of this depends on the system. Yes, if you really want to do character driven it helps to not be too lethal, but lethality is a product of system mastery and choice. And something like 2e really survivable after the first few levels if you aren't trying to push for lethality and challenge as the primary aesthetic. High level AD&D characters have massive amounts of hits points relative to the monsters they encounter, no crits to worry about, and as long as you don't hit them with save or die too often, they are really hard to kill. All you really do is feed the players challenges that are a couple levels below what you'd do in a more challenge-oriented game.
Maybe, TB2 can be pretty deadly, but I think even there it isn't overwhelmingly so. But in any case, I think the genesis of the situations in the sort of narrative play we usually speak of is not the same as what you have in mind, generally. It can be hard to draw distinct hard lines though. Still, lack of lethality is not, IMHO, a necessary feature of narrative play. I think a very lethal game of that type would require some sort of 'threading' mechanism aside from PC to kind of carry forward the narrative, but it seems possible to do.