See, on the one hand, the vast majority of people I know who play OSR games, talk about OSR games, make OSR games, etc. all seem far more interested in being "the Barbarian." They talk about how modern high fantasy gaming is too caught up in these drama-centric stories of grand, world-shaking stakes and superheroism and PC-focused plots and blablabla. That their preferred way of play, and the true ways of old are the Sword-and-Sorcery tradition of, to put it bluntly, murder-hoboism. To be a little more generous, that D&D should be a picaresque. In a low fantasy world where morality is grey and lethality is high, the "heroes" are wandering sell-swords and rascals scraping by on a few copper coins at a time. Every time they come into a significant fortune of treasure they blow it all on booze and hookers immediately. They never stay in one place for too long, and they generally get by on their cunning. If they do get permanent boons, it's usually in the form of powerful magic weapons and blessings. "All characters are rogues" you might say. Conan the Barbarian, Fafhrd and the Gray Mouser, Cugel the Clever, and so on are our archetypal examples. But also, like, the Wandering Ronin, the Man With No Name, Hellboy, Geralt of Rivia, the heroes of Manly Wade Wellman, etc. Gold-as-XP and Carousing rules are the pillars of design elements that support this style of play, because they reward you for stealing treasure above all else. The essence of adventure to these players. They play in sandboxes because they need the freedom to explore.
On the other hand, many of the actual old-timers who played D&D back in the 70's and 80's definitely seem like their idea of the hobby is being "the King." They talk about the tragedy of modern high fantasy gaming missing the rules and procedures for domain-level play, and they trade stories about the complicated political intrigue/shenanigans of Greyhawk and Mystara. A lot of them were wargamers, and the idea that mass-combat rules should be included as a core part of the game was simply a given to them. Birthright and Council of Wyrms were made for these gamers. Character advancement usually wasn't much more complicated than a couple measly bonuses to your raw numbers here and there, but at a high enough level you'll probably earn a castle, tower, temple, or some other kind of dominion. That kind of thing can be a confusing class feature to someone coming from modern gaming. A castle doesn't help you in a boss fight with an arch-devil, so what good is it? Well, it makes you more socioeconomically powerful. It opens up new avenues of adventure and gives you much more powerful tools for problem solving. Access to a ship means freedom of travel, and freedom of travel means more freedom to choose your destiny. If you get into politics, eventually you can literally send armies to raid dungeons for you. The kinds of high-level boons you're going for would be vehicles, followers, contacts, favors, a stronghold, access to a natural resource, princesses, etc. Even Matt Colville, someone who normally traffics firmly in the New-School, is still influenced strongly by his 1980's grognard roots and wrote a 5E supplement for this called Strongholds and Followers (it's pretty good), and is in the middle of a sequel called Kingdoms and Warfare (it looks better). There was a point in time when it was just understood that D&D had "late game content" and it looked like this. There is a designated endgame where you aren't dungeoncrawling anymore and are instead fighting wars. There was also a midgame stage where you might command a small "warband" of followers. Y'know, like the Merry Men from Robin Hood or the Brotherhood Without Banners from Game of Thrones. Or... the pirate crew commanded by Conan in between his days as a barbarian and a conqueror. Huh.
See, I think the "Barbarian" players massively control the narrative, but the "King" players have a solid claim to make here. It's not actually as though the Sword-and-Sorcery genre didn't have plenty of content clearly in the vein of King-adventure rather than Barbarian-adventure. The second-most important Sword-and-Sorcery hero is Elric of Melniboné, who, from his very first adventure, is a literal king of a kingdom. I'd throw Prince Valiant in as well. And you know, you could argue that Gold-as-XP is built for this style of play equally well if not better. After all, the reward for reaching higher levels is pretty much always stuff that costs tons of money. Is it so outrageous to suggest that the idea going on here is, "XP is an abstraction of the process of the adventurer gaining enough gold to buy a castle"? Even if you let the players spend their treasure as they please, the higher level they get then the more and more they'll be drawn to luxuries like strongholds, airships, war elephants, and so on as their primary money sink. They play in sandboxes because they're indulging in campaign-level play.
When you ask for decent "King gameplay" rules these days, you usually get pointed towards either BECMI's rules (which I'm not a fan of ) or Adventurer, Conqueror, King by Alexander Macris (who I'm really not a fan of). Many minimalist OSR games are content to offer little-to-no advancement guidelines, and while they don't forbid domain gameplay... they don't exactly facilitate it well. When everything on the equipment list is "stuff a knave would use when dungeoneering" then I feel comfortable saying your game is basically just about dungeoncrawling and not much more. Now and then you get a little bit from games like Into the Odd or Mausritter, but arguably not enough to sustain a long-term campaign focused on this kind of gameplay.
So, are you more of a Barbarian or a King? And if you're a Barbarian, have you ever actually tried playing like a King? I want to accommodate both playstyles and preferences equally well, but one of them is certainly trickier than the other.