Books are not games.
Systems are there in a game because they need to balance the gameplay and give the player interactivity with the world. A reader does not interact with the world; they read about it. There is no input that needs any type of system. The same is true for the author: you make the rules, you balance them; including a system is nothing more than introducing an element that will make your work harder, your story more prone to plot holes and mistakes (call it bugs), and other issues.
Every character's skill, be it with the sword, book, foresight, or just the strength in their pinky finger, can all be realized without including a system. It is nothing more than a glorified word count booster. I have not read a story yet where if the system was thrown out of the story, it would become unreadable.
Everything people use the system for can be replicated without including it, and the story would stay the same. Or, in many cases, be better because it lacks a system.
I don't agree with you, a system can serve several purposes. They can serve as a framework to allow the acquisition of new powers as a reward for the type of behavior that is interesting to read about, but wouldn't necessarily give new abilities. Think about it, how much must be going on, on a technical level, to allow someone to perform something like necromancy. Healing. Heck, even just flight. If your story doesn't revolve around the technical aspect of how various powers work, but you still want your characters to gain access to them, rewarding them for taking actions that make the story interesting, a system is a very easy way to do that, without having to reinvent the wheel. It
is weaker world-building wise than an alternative, but if you don't want to focus too much on the how, but rather what can be done once you have a power set, a system can be a useful tool. Depending on the system, they can also serve as a way to tangibly reward unique characteristics and actions of your characters. Ultimately, systems are a tool, in the wrong hands a crutch, but when applied correctly can allow one to access certain story structures that would otherwise be impossible or convoluted.
And there
are stories, good ones, that wouldn't function to the same degree at all if you ripped out the system. Systems can act like an engine, driving forward a character's growth, in power, but also in handling the change that comes with power, and the risks with seeking power. See Azarinth Healer. They can act as a catalyst, a structure to make it easier for a character to grow from struggle, see Unbound. A system can also act like a character in and of themselves, woven into the function of the world and serving as a large foundation to the plot, see Amelia: Level Zero Hero, or Let's Not [Obliterate].
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Now here are my thoughts when it comes to building your system. Firstly, avoid too many numbers. A lot of the issues people have with systems comes from the meaningless lists of numbers. Number goes up, quite frankly does nothing substantial, and after a while just feels dry, something to skim over. Levels and stats are meaningless. At least, if you overuse them. Don't use levels and stats as the means by which your character gets stronger. Grinding gets boring, slow growth of skills and stats has no observable benefit to the story than if you just, didn't show the numbers but let your character develop their potency through less heavy-handed means. If you're going to use numbered stats and skills, make sure that the it's the number that reflects the character's growing competency that you show in story, rather than the number going up that artificially inflates the character's ability. Skill levels are useful to track a character's level of mastery, but don't get caught up in like, skills that grant number bonuses to stats, increasing the bonus as you level the skill, that's meaningless. Skill levels should provide a point of comparison that allows a reader to intuitively understand how skilled the character is relative to other characters. If the average level of Sword Mastery among knights is 5, and the MC has the skill at level 7, that tells us where to expect our MC to stack up against them, in that category at least. But if that's all your system does, it's not worth it.
Personally, I prefer a more, milestone and special-power based system. Where levels serve as, essentially, progress bars to the next milestone, which either unlocks new abilities, or expands old ones, letting them be applied in new ways, and stats just serve as the prerequisite to being able to face tough enemies, but not the source of the characters power. That kind of progression is far more interesting than just, 'Iz slightly better at swinging sword, now' 'Has 50 strength now!', etc. The abilities this kind of system grants need to be something
more than what can just be acquired without a system, or simple magic. If all the system is gonna do is track how well someone can swing a sword or throw a fireball, it's just telling instead of showing, it serves no purpose, find a better way. A system needs to serve as a way to make something that wouldn't be possible otherwise for your story/characters, possible. And, abilities granted by the system should be personalized by who your characters are and the actions they've taken, what they've gone through, challenges they've overcome. If your powers are too generic, if everyone has the same or similar abilities, they start to lose their significance.
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I just wrote all that, but my brain is kinda sleep-deprived melty mode right now so it maybe wasn't the best, I'm just gonna copy paste something I wrote a bit ago on the matter here, there's some overlap, don't care
An important thing to consider when discussing Systems is where did it come from? What are it's limits? Is it a fundamental law of the universe, or was it created by someone? For what purpose? This can drastically change things, because if it's fundamental, then it might not be exploitable and there might be no theoretical limit to anyone's growth, but if it was made by someone, depending on who and why, it could have faults that could be exploited, inherent imbalances, limits. The System could be neutral, an ally, or an enemy, depending on why it was made. It could be omnipotent and omniscient, or it can be constrained.
And whenever you write a story with a system, you should first ask yourself if you can tell the story you want to tell without it. If the answer is yes, then you shouldn't bother with a system, it'll just bog things down with meaningless numbers that don't actually mean anything. If a story has a system, it has to be somehow relevant to the plot or essential to the world, either by allowing things that otherwise wouldn't be possible for the characters/world, by acting as a pseudo character in and of itself, by shaping civilizations in the world, or something else.
It's also notable that not every system
has to have numbers, or even progression. A system could be as small as everyone gets one skill at adulthood, for example. There's no progression, but it could still have large implications in world building, with inherent inequalities based on what kind of skill you have, class systems based around that. Having a single skill might make characters need to be more creative about it. And it can serve a roll to give characters unique powers that would otherwise be difficult to fit into a setting or explain just how they work, or would be too difficult in practice for a person to actually use without 'system assistance'.
Personally, I prefer systems that are light on the numbers and numbers of skills, and focus more on the unique powers afforded by the skills, beyond a the simplistic stuff like 'oh, increase fire damage by 1% for each level in this skill'. That type of skill is just not narratively interesting, and it's hard to see the effects in the story. It might as well not be there.
Skills should have direct, visible effects in the story, and advancing the skill should have tangible, immediately obvious benefits. That is much more satisfying for a reader than just, 'number go up'. Eventually, number go up becomes boring and just gets glazed over. Skills having levels is okay, but I believe they should not be the sole thing going on. I believe that levels should act more as progress bars to the next milestone, which fundamentally alters or expands the skill in some way.
Skills are more crucial to a system than stats. It's the skills that make or break a system, by both meanings of the word. Read enough LitRPGs and stats start to lose all meaning.
If you do decide to use stats in a system, you should make it very clear in-story, through action, the impact those stats have. For a stat going up to have meaning, you have to very firmly and intentionally demonstrate time and time again how those stats make what would otherwise be impossible, possible.
You should be very aware of what kind of power scaling you intend for your system as well, and where that power comes from. Is it the skills that propel people into the superhuman, or the stats? How superhuman can people become with the system? Capable of wrestling a mammoth? Capable of punching a planet into oblivion? The larger the scale, the more careful you have to be with big numbers, because eventually every big number looks the same. You might want to be more reserved with increasing numbers, but make each one count more. Or, you could have different 'stages', and when you advance from one to the next, your stat display shrinks down, not actually decreasing the output but simply putting the display into perspective for the stage of power you're on.
I still personally don't think stat numbers is very good, personally, and you shouldn't just replace it with a different-looking but identical in practice system either (like letter grading). It's not the inching forward growth that's satisfying, but the milestones (at least in my opinion, but I don't think it's an uncommon one?), so a system that capitalizes more in milestones will be more satisfying.