Taking over the world is fun. It’s so much fun that entire genres of video and board game can present world domination as the end goal and on basis of that alone, players will be engaged. The main campaign of an FPS will need to present you with some kind of story or characters to keep most (though not all) players on board, and even those that don’t tend to have a powerful sense of atmosphere to fill in that gap. DOOM didn’t really have a plot past the introduction (found in a .txt rather than in the game itself), but it felt like a playable heavy metal album cover, and that was enough. Until 2016, anyway, when DOOM got itself a parody of a plot, but still an actual plot. Galactic Civilizations, meanwhile? Crusader Kings? Civilization? “This is a map. Make it yours.” Done.
So it’s no surprise that people want to take over the world in D&D, but there’s a bit of a problem there. See, you can go on adventures to take over a kingdom just fine. You loot dungeons to amass wealth, and you infiltrate the court, and you scout out the wilderland to find places to establish a rebel hideout where you won’t be easily found, and you storm a boat to save the dark lord’s rebellious daughter from an arranged marriage that would secure his alliance with the kingdom of Sinisteria across the border, and then at the end you capture his castle, and these are all either roleplay-heavy intrigue plots or they’re exploration hex crawl-y things or they’re good old dungeon crawls, but all of them are within the scope of three-to-seven heroes getting things done by personally being awesome.
From now on, though, you’re nailed to this kingdom, aren’t you? Like, you go and conquer Sinisteria, but you do it with a giant army. So anytime you storm a dungeon, there’s like a thousand dudes storming it with you. A lot of characters might not have any good motivation to stay on the front lines when you’re probably not contributing all that much to the success or defeat of those thousand dudes. If you’re dedicated to cash, you can probably make a lot more setting up trade routes and soaking in a 5% cut from taxes than personally storming enemy castles for a share of the loot, especially since 5% of that loot will come back to you anyway when victorious soldiers spend it all in shops that you tax (or even own). If you’re dedicated to justice, you’re probably going to do more good acting as a judge in your capital’s hall of justice and trying to set as many fair and equitable legal precedents as you can in a day. If you’re in it for the glory, then you’re probably better off on the front lines, but most of the other common adventurer motivations break down once you own an army that’s significantly more important on a battlefield than you are.
What you want out of a world domination campaign is a setup where things like mass battles and kingdom management happen in addition to dungeon crawling and overland exploration and such. If you want that, you want a world that operates on spheres of influence.
A sphere of influence is a means of a nation to exert power and influence over distant areas without occupying them directly. It usually comes up in heavily trade-based societies, like the modern global society or Ancient Greece, where invasion of or longterm occupation of most enemy territory is, for whatever reason, untenable. Instead, spheres of influence work by treaties and proxy wars that seek to convince a regime that controls valuable resources or a strategic location to sign a treaty with one power to the exclusion of others, granting that power (and possibly other states already within the sphere of influence) access to the resources or position commanded by that regime. If the local regime won’t cooperate, the bigger power might try to replace them with someone more open to the deal. Rival powers, meanwhile, want to prevent that from happening and also do the same to local regimes already on the original power’s side.
Let’s illustrate with an example from the Forgotten Realms. Say that Waterdeep and Zhentil Keep are competing spheres of influence (depending on how you interpret the lore, this is totally how the Lord’s Alliance and the Zhentarim functioned back in 14th century Faerun). Waterdeep’s sphere of influence is a formalized military alliance called the Lord’s Alliance. Zhentil Keep’s sphere of influence is an insidious conspiracy in which lots of allegedly independent nations are secretly run by puppet regimes called the Zhentarim. In the 14th century, most of the Moonsea was in Zhentil Keep’s sphere of influence, and most of the Sword Coast was in Waterdeep’s. Now, Zhentil Keep isn’t going to try and conquer any part of the Sword Coast. There’s the Anauroch Desert in the way one direction and Cormanthor, the Dalelands, Cormyr, and Sembia in the other. What they will (and often did) do is attempt to bring potentially friendly regimes within their sphere of influence.
Kryptgarden Forest is full of evil fey and a big old green dragon, among other nasties, and is right on Waterdeep’s doorstep. If Zhentil Keep can find some way to entice that green dragon, the local king or queen of the dark fey, or both to join the Zhentarim, they have gained a powerful strategic advantage. In the event of open war between Zhentil Keep and Waterdeep, Zhentil Keep only needs to cast one Sending spell and there will be an army pointed straight at the enemy capital (and remember, just because a sphere of influence system doesn’t have the troops to conquer doesn’t mean they don’t have the troops to raid – raiding warfare and the sacking of cities was plenty common within and between ancient Greek spheres of influence). Waterdeep, meanwhile, will have to march forces past Hillsfar to reach Zhentil Keep for a proper retaliation.
Speaking of Cormanthor, as of 1372 it is back in the hands of good elves and taken from the hands of Lolth-worshiping drow, and these were generally friendly to the Lord’s Alliance. They were in the Waterdeep sphere of influence, but not very deep in it, and the Zhentarim could reasonably convince them to declare neutrality, making it difficult for the Dalelands or Cormyr to attack or influence the Moonsea region. For that matter, some or all of the individual member states of the Dalelands could be convinced to declare neutrality, since they too are only in the outer reaches of the Waterdeep sphere of influence.
In order to oppose these actions, Waterdeep needs adventurers. They need adventurers to disrupt whatever shenanigans the Zhentarim are getting up to in order to get the rulers of Kryptgarden on their side. Failing that, they need to stab the rulers of Kryptgarden in the face and install a new regime, one that is at the very least neutral, and preferably friendly to Waterdeep. They need adventurers to foil Zhentarim schemes to install a new neutral (or even Zhentil-friendly) regime in Cormanthor. They need adventurers to help sort out the troubles in the Baldur’s Gate region before the second most powerful city of the Alliance loses confidence in the ability of that Alliance to defend its members and leaves. They don’t need armies for this. Their armies are insufficient to actually attack and occupy this many different locations, and just trying to occupy a foreboding location like Kryptgarden would go very poorly for a bunch of zero-level schmucks in scale armor. They need small, fast-moving, very powerful strike teams of high-level heroes to adjust the balance of power to favor whichever existing local faction is most favorable to Waterdeep.
The important thing here is that the PCs have very important things to do as adventurers, and those things are so important that they might reasonably consider doing them even if they personally rule Waterdeep. Even if they have become fully 100% of the Masked Lords (or they’ve just overthrown them completely) and now directly administer the city, they are still better off personally going into Kryptgarden and killing that dragon before he joins up with the Zhentarim rather than sending an army, because if they send an army odds are excellent that they will lose that army and the dragon won’t even bite it in the process. They might not even reach the dragon.
Better still, this way of doing things is pretty compatible with newly released adventure paths with minimal tweaking if you want to oscillate back and forth between published content and home-made. Since your standard answer to all problems is not “throw an army at it,” you don’t have to pull any shenanigans to force players to actually go on adventures. Storm King’s Thunder, for example, works almost perfectly as-is. The various evil giant warlords conspiring against the titular storm king are all being backed by an enemy sphere of influence (the Zhentarim don’t work because they’ve gone anti-hero in the 15th century, but maybe the Red Wizards of Thay or the Netherese), and you want to rescue the storm king and defeat his would-be usurpers in order to convince him to join your sphere of influence with some kind of formal treaty of friendship between the giants and Waterdeep (or Baldur’s Gate or Cormyr or whatever the capital nation of your sphere of influence is). Princes of the Apocalypse takes place in the Dessarin Valley, which you are either protecting because it is in your sphere of influence or in an effort to convince you to join (and really, once local authorities are dependent upon you for protection they are in your sphere of influence whether they like it or not, because all you have to do to destroy them is stop preventing other things from destroying them).
Using spheres of influence, you can go on an adventure and when it is done you have made your colored blob of the map slightly larger (or a whole lot larger, if you’re impatient). If you want full points, you’d also want to add in some mass combat and kingdom management rules on top of that, but the basic conceit of the sphere of influence is enough for a perfectly satisfactory game of world domination using the D&D rules as written.