What can shounen anime teach us about gaining experience?

One thing that fascinates me the most about games is how much of the rules are, as a matter of course, arbitrary. This is for a reason—without clear, deliberate rules, the game becomes too loose to be uniformly played. We need to be able to quantify some rules just to pull off the parts of the fantasy that matter—but the more you think about how we quantify them, the more it reveals the game’s assumptions about how those things function and how we unlock the fantasy within those rules. 

We need hit points because it matters whether you have taken a glancing blow you can wince your way through, or if a severe wound has laid you low. We need death saves because it matters whether you're following the light at the end of the tunnel or just lay still on the ground waiting to be revived. And we need experience points because it matters that we are getting better at the things that define us, that we are growing in skill to the point where we can outdo our former selves and overcome even greater challenges.

But to my mind, “experience” is the most interesting—and most baffling—part of the fantasy of gaming. At its best, “experience” imagines learning new and radically powerful skills, and honing the ones we already know to their finest points, as something we are simultaneously working toward gradually and gaining in powerfully sudden ways. One day, you're casting your eleventh Fireball spell in a dusty dungeon, and the next night you suddenly realise that you know how to Banish something.

Surely the narrative can find a way to spin how you've developed these skills? In Dungeons & Dragons, from whence I draw this reference, each spellcaster class has its own logic. Wizards are performing the act of learning, making observations in the real world and jotting them down in short rests--but how actually dynamic is that learning, in a mechanical sense? Is a Warlock actually growing in power, or simply being trusted with more of it--and is there just as much narrative space for them to earn that power by performing their loyalty as there is by gaining magical prowess? Doesn't it make a bit more narrative sense for a Sorcerer to learn how to better cast the spells they're already blasting out before playing around with new, and potentially volatile ones? Martial classes follow even more uniformity--most of the time, you're simply doing something you already know, but harder or more often--but how does a fighter “learn” to Action Surge, and why can't a Ranger “learn” the means to track an additional Favored Enemy?