I agree with you. I don't mind using attacks myself, or necessarily using game mechanics. My question is whether those game mechanics can be translated into something that makes sense in fiction. Sometimes they can, and sometimes things are lost in translation. And as for attacks, I am more concerned with how attacks would actually work and look in a real life context.I like the example about Shadow Ball and Shadow Claw. As for move limits, I also agree with you. Though I thought the limit was six. Then again I've never played the games, so what do I know? I see some sense in that the move limit corresponds to memory, and attacks may require constant practice not only to make them instinctual and natural, but to keep the Pokemon from getting rusty. But some attacks shouldn't count. For example, Tackle. It's rather basic, so it shouldn't tax memory. Or Water Gun for a water Pokemon (if they have the organ for it, it should be natural) or Flame Thrower for a fire Pokemon.
On the subject of real world battles, I actually came up with an interesting strategy myself. I have mentioned it in another place, but I am playing around with a story involving an Ash clone. Don't expect the story to come out any time soon, I am just playing around, and I have to definitive plot. But in that story, the clone (who I have named Ace) had a Gengar, and I thought of a way for it to have a powerful advantage over fire types, and defeat them with ease, even though fire types don't have a particular weakness against ghosts.
You may recall that Gengar is solid for the most part, but has the ability to become intangible, aka, pass through solid objects. If you read the Bulbapedia entry, it also mentions that Gengar's body acts like a heat sink, so the spot it stands on suffers a temperature drop to negative ten degrees. With that in mind, Gengar could severely weaken or flat out defeat a fire type simply by walking through its opponent. The sensation of cold is simply the process of an object stealing heat from another, warmer object.
If Gengar becomes intangible, and passes through a fire type, its body would sap heat right out of the fire type. That would no doubt be extremely unpleasant for the opponent, if not weaken them. And by continuously doing that, Gengar could possibly even incapacitate them, without breaking a sweat. It's a good strategy, but not something that works in game.
And about type advantage again, I think it's important to come up with why some types have advantages over others. It's not too hard at times, because the type advantages are usually grounded in some real world logic, but things like the "grass and ground types protect themselves from electricity by grounding it" is a perfectly logical answer that allows for a better story or fight scene. TV Tropes has a fanon Pokedex that tries to go over the special characteristics of each type, though they haven't gotten far, and I am not sure I agree with the ghost type entry. But that sort of thing says something about how Pokemon work.
For example, hearing that Dragon types are weak to Ice type attacks, that would suggest to me that Dragon type species are cold blooded, and have the same crippling, immobilizing weakness to cold as actual lizards.
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