You can hold, say, seven items in your mind while considering any subject. This vastly limits your ability to consider any complex system.

Really? A dubious notion in the first place, but untrue by the counterexamples of folks who go above 4 in dual N back.

You seem to have a confused fantastical notion of working memory ungrounded in neuroscientific rigor. The rough analogy I have heard is that working memory is a coarse equivalent of registers, but this doesn't convey the enormity of the items brains hold in each working memory 'slot'. Nonetheless, more registers does not entail superpowers.

Alternate example: a novice chess player has to look at every piece, think about likely moves of every one, likely responses, etc. She becomes overwhelmed very quickly. An expert chess player quickly focuses on learned series of moves, known gambits and visible openings, which allows her to see several steps ahead.

Chess players increase in ability over time equivalent to an exponential increase in algorithmic search performance. This increase involves hierarchical pattern learning in the cortex. Short term working memory is more involved in maintaining a stack of moves in the heuristic search algorithm humans use (register analogy).