You may be on to something. Sure human working memory (insofar as our measurement tools can tell us) seems to be limited to single-digit datasets, and long-term (that is, persistent) memory is poorly understood but research portrays that it's a pile of more or less random bits.
It's a subject of professional interest to me for decades, what impresses me is how much isn't known about how our built-in "computer" actually works. Above all neurons are extraordinarily intricate structures, and beyond that the contributions of non-neurons in the brain appear to be considerable. Given that the brain contains at least 100's of millions of participating neurons organized in a complex hierarchical network, no wonder it's still not possible to adequately account for many relatively simple phenomena let alone the emergence of towering genius.
Indeed our wetware is collectively both more capable (and more limited) than we generally appreciate. Definitely we can't predict where genius will arise, it always seems to surprise when it happens. To say it's a miracle may be naive, but perhaps that just expresses wonder and gratitude for a rare, random and highly fortuitous event.