That's an interesting take, but it definitely makes sense. I've never played KH. Gonna do some thinking out loud.
I think the four general dials you can crank with difficulty are leniency, complexity, execution, and options. And which dials should be cranked and when are definitely game-by-game.
(Fucking up is more consequential)
Increased time between checkpoints
Making mistakes more punishing
Limiting the player's access to vital resources
A lot of popular self-imposed challenges fall under this category. Using Pokemon as an example, permadeath runs are really popular, but on a less extreme end, I personally don't like using healing items in-battle because the leniency they grant makes the game less fun for me.
A huge advantage of this style of difficulty modification is that it's really easy to implement. To the extent where you can modify a game's leniency without even needing to touch the game's code.
I think the problem that ppl sometimes run into with this type of difficulty modifier is that it can result in tedious gameplay if it doesn't add to the game's experience in some way. Like, if the gameplay at a higher difficulty setting feels like the gameplay at a lower difficulty setting and the only difference is that it takes longer, then something went wrong. And that something could be anything from the edited numbers being poorly balanced to the game's fundamental systems just not scaling well with difficulty.
(It is easier to fuck up)
Mechanics that require precise inputs from the player (such as button combos, tech, parrying)
Decreasing the window of time players are given to react.
Increasing the pace of the game.
I usually see this type of difficulty accomplished through employing more aggressive or risky playstyles. In an action game, this might look like staying on a boss's face the entire fight, while in a strategy game, it may look like trying to complete a level in a low number of turns.
The main benefit to this style of difficulty is that there really isn't a ceiling to how high it can theoretically go. The main drawback is probably that enforcing this style of difficulty can be really awkward and a lot of components to it can consist of knowledge checks.
I think the two best ways to design this type of thing are to either implement systems that encourage the player to take up self-imposed challenges or present the player with challenges that force them to utilize high execution mechanics.
(There are more ways to fuck up)
Manually altering the individual challenges a player is expected to face (such as changing the moveset of a boss or the layout of a level)
Introducing new systems to manage
This one probably makes for the best soundbite. But it's also a very situational and resource-intensive way to up the difficulty. There's also a cap on the exact amount of challenge you should be introducing like this since the harder something is, the less people will be able to enjoy it. There's also the major risk that the new stuff created for the purpose of increasing the difficulty fails to be enjoyable, fails to feel like part of the main gameplay loop, fails to raise the difficulty by a consistent amount, or lends itself to the question of "why aren't these things not part of the lower difficulty gamemodes?"
I think Into the Breach does a good job at this, where it has two separate difficulty scales; one affects margin for error while the other is strictly complexity. Since its a strategy game about defending points of interests from swarms of enemies, where major parts of the strategy involve knocking enemies around and utilizing environment hazards to your advantage, having the option to increase the types of enemies that can spawn or increasing the variety of environmental hazards feels like a natural step in progression more than anything. This is definitely helped by the game being a Roguelike, so individual playthroughs aren't going to take super long.
This method of increased difficulty can be good, but it's probably overrated by gamers. Increasing complexity in service to difficulty is inherently inefficient and polarizing. The problem is that increasing the game's difficulty should be in service to making the game more fun for players who want to master the game's mechanics. Introducing new mechanics for the player to learn, but it doesn't inherently ask the player to master anything.
(You have less ways to approach problems)
Removing mechanics, potentially dressed up in the form of a gimmick, character, or restriction
I usually see this in the form of self-imposed challenge runs or restrictions. This sort of thing tends to result in you playing the game differently than usual. Sometimes it's super novel and weird, like the challenge runs where you beat various Mario Games without jumping, which tends to result in a mix of weird tech plus puzzle solving. Other times it's just really boring, like a lot of the Dark Souls runs where you're limitted to only using a specific weapon type (I'm mainly thinking of the Bow Only runs, where it just makes fights slow and uneventful). Personally, the version of this I find the most fun is fighting bosses without access to mobility upgrades that the game expects you to have (like taking away your Dash).
Whether this is actually fun varies heavily on the game and limitation in question. In the best case scenario, you get to experience the game in a novel way. Worst case scenario, you're just doing the same thing but it's more annoying. I think the main reasons this type of thing isn't usually built into games as methods of increasing difficulty is because they involve playing games in unintended ways and because trying to enforce it would be a massive "no fun allowed" sign. Also, taking away major mechanics tends to result in wildly unbalanced gameplay and extremely wonky difficulty curves. The best example I can think of to demonstrate this is from Celeste, where there's a hidden collectable you can get by beating the first level without dashing. If you go for it, half of the screens are virtually unchanged and the other half require you to do insanely precise maneuvers that are otherwise found exclusively in mods and speedruns.
I'm pretty sure when this concept is used, it just isn't framed as a difficulty setting. Instead it's either framed as a temporary part of a level or as a mechanic or item you can enable/use to decrease the difficulty.
But yeah, each method of increased difficulty has its own effects and reasons to or not to employ them, but it definitely makes sense that messing with leniency is by far the most common way for games to modify their difficulty.
