But I think it's a good fit. And I'm going to explain a bit about why.
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Here is the default plotline of most heroic fantasy narratives:
'One day, the Forces of Darkness found a big stick. They used the stick to beat everyone up! It was terrible! So the Forces of Light had to go on an Epic Quest to find an even bigger stick, which they used to beat the Forces of Darkness back down again. Then everyone lived happily ever after, except the Forces of Darkness, who had all been beaten to death. The end.'
Might makes right. The good guys don't win because they're good; they win because they are able to attain a greater capacity for acts of spectacular mass violence than their enemies. The world remains shackled to a treadmill of violence. Viewed with even the slightest cynicism, the whole narrative starts to look deeply suspect, the kind of story that victorious empires always tell about their origins: 'Of course we're the good guys! We won, didn't we?' This is probably one reason why world-weary amorality is so common in OSR fantasy games; strip away the genre conventions and it's easy to see the Forces of Light and the Forces of Darkness as little more than two interchangeable warbands, flailing away at one another with whatever physical and rhetorical weaponry happens to come to hand.
Romantic fantasy narratives, by contrast, are usually built around defeating evil by means other than overwhelming lethal force. Consider a story like Ghibli's Spirited Away. Chihiro is thrown into a supernatural world dominated by cruelty and injustice, but she doesn't defeat it by hoarding magical power-ups until she's strong enough to punch Yubaba in the face. She wins because she's brave and clever and empathic enough to make friends and build alliances, and at the end of the day her courage and emotional intelligence prove to be more than a match for Yubaba's evil sorcery. By the end, when she leaves Yubaba's realm, everyone is cheering for her - even the frog- and slug-people who have been making her life a misery since she arrived. She has changed her world for the better. She didn't even have to beat anyone to death along the way.
Now, you don't have to like those kinds of stories. You might even think they're 'unrealistic'. (It's certainly true that, in reality, love and courage don't always win out - but then, in the real world, overwhelming violence doesn't usually do much real good either, does it?) But if that is a style of story-telling you're interested in... why would you use OSR D&D to run it?
1: The reaction System
If you're using the old B/X reaction roll system, there is only a one-in-thirty-six chance that any given monster encounter goes straight to violence. Anything else gives you some room to manoeuvre: to talk, bluff, make a bargain, offer a bribe, whatever. If you want a fight you can have one, but you almost never actually have to fight. (And hell, even if they do attack, you can always just run away.) This is very different to later editions of D&D, which assumed that monsters would always attack on sight and usually fight to the death.
If you use the reaction system, then instead of the dungeon becoming a series of tactical combat challenges, it becomes a network of social challenges. What does each group want? What does it need? What can you offer them, and what can they offer you? With a bit of quick thinking and a lot of heart, you can talk your way through a dungeon much more effectively than you could ever fight your way through it.
2: The morale System
Even if a fight breaks out, the B/X morale system ensures that only crazy fanatics and mindless undead are actually likely to fight to the last man: everyone else is much more likely to try to run or surrender once you start killing their friends right in front of them. As a result, violence tends to be limited: bullets fly, bodies drop, the balance of power changes, and then you go back to negotiation again. You can kill 'em all if that's what you really want to do; but if you don't want that, if you'd actually quite like to find a better solution, then the morale rules give you a way to end fights while there's still someone left to make peace with.
3: The combat system
As the saying goes, if you've got a big enough hammer, then everything starts looking like a nail. If you've spent hours building your character from half-a-dozen sourcebooks, and you have a giant heap of hit points and a list of combat abilities as long as your arm (as can easily happen in certain other editions of D&D), then why wouldn't you want to solve problems with violence? By allowing players to create characters who fight like action heroes, later editions also encourage them to think like action heroes - and action heroes solve all their problems by killing people. Usually lots of people.
OSR D&D isn't like that. At first level you probably have about four hit points. Even at third or fourth level you can still be killed outright by a couple of lucky hits. Getting into anything resembling a fair fight is a terrible idea.
For the 'amoral sword and sorcery' style of OSR game, that acts as an incentive to seek out unfair fights: poison them, ambush them, stab them in the back. That's great. But it can also work to incentivise less violent solutions. Like Chihiro, PCs don't have the option of simply brute-forcing their way through situations. They need to find other, better ways to succeed.
4: The retainers system
I love hirelings and retainers. Again, if you're playing grubby amoral OSR murderhobos - and you can! There's nothing wrong with that! I've done it myself! - then your hirelings and retainers are luckless saps who you bring along to do your dying for you. But they can do other things, as well.
Later editions of D&D, with their higher-powered protagonists, encourage PCs to rely on no-one but each other. The model is the superteam or the spec ops squad: a small group of badasses who are so much tougher than ordinary people that anyone else would just get in the way. OSR D&D, with its squishier PCs, isn't like that. Every other person you have with you - even ordinary, 0-level people - can make a real difference to your survivability. You can't just wander off on your own: you'll die out there. You need other people.
OSR PCs build communities. Each PC has their own hirelings and retainers; a party of six PCs could easily have another twelve or fifteen people tagging along with them. This ensures that each PC is enmeshed in a whole network of relationships with other people, people who they rely upon - and who rely upon them - in life-or-death situations. Rather than just an atomised individual, caring about nothing except his +3 sword and his bag of loot, the PC has to become a leader, a friend, a companion-in-arms - because if they don't, hireling morale will plummet, and they'll desert you when you need them most.
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The cumulative impact of these four systems is to create situations which heavily favour relationship-building and non-violent forms of conflict resolution. Of course there will still be fights; of course the PCs will occasionally just say 'fuck it' and shoot a bunch of guys in the head. Of course there are going to be some people who just need killing. But mass violence isn't the default solution, and it usually isn't the best solution. The best solution is talking: treating your potential enemies like people, negotiating, finding common ground. With a bit of work, you can turn them into allies instead of enemies, leaving the encounter stronger than you were when you came in.
And if that doesn't work, and they really won't listen, then you can always circle back later, wait until they're sleeping, and murder them in their beds. Romantics can be pragmatists, too!