eurus is a Mystery, and the Sherlock Holmes stories are about mysteries
the core of the original Holmes stories was the way they were rooted in rationality. not necessarily perfectly. they had their issues, of course.(but they were surprisingly good for the time period. as i discovered when i read dracula. but i am heroically not ranting about bram stoker right now and you all should be thanking me). however, fundamentally, Sherlock Holmes was a rational being.
even when conan doyle was being fooled into thinking fairies were real, he recognized, quite wisely, that (to quote him in a different context) "the created is not the creator". in the sussex vampire Holmes himself says that "[n]o ghosts need apply". fundamentally, conan doyle's Holmes is a creature of rationality, predicated on the reassuring belief that there is always an explanation, that the Things at the edges of polite victorian society can be explained, deconstructed, analyzed; that they are, if not perfectly rational, comprehensible. there is no magic, there is little unexplained; the stories have their factual errors and inconsistencies, but the fundamental premises are not outlandish. everything has an explanation. the world can be placed into nice neat boxes and given labels. it's a very reassuring worldview.
to put it simply: the Sherlock Holmes stories are about mysteries, not Mysteries. mysteries follow some unspoken, higher-up rules, beliefs about how the world operates. perhaps there is a murder; but a reason can be found. there are clues. things occur in chronological order; perhaps they are not revealed in chronological order, but they happen in that, there are no time loops and no one is in two places at once. there is such a thing as the impossible. there are limits to things that can be done. Mysteries take those beliefs, beliefs you may not even realize you had, and explore what happens when those rules are broken. they are creatures of horror, more than mystery. they do not owe you explanations or rationality.
and at first, Sherlock was a fine mystery show! the cabbie in ASiP didn't use dark magic. it required some suspension of disbelief, but it was reasonable, believable, the suspension merited by the nature of the stories (i assume they got bits of the uk legal system wrong, but it's not as if crime stories set in the us are well-known for their accurate portrayals of the legal system.)
but then along comes eurus, who is a clear Mystery. she takes the basic principle of Sherlock Holmes -- that there is always an explanation, that even the most seemingly perplexing things can be comprehended, that even the things that appear to break the rules really do follow some rules, that the eldritch beings at the gates are really phosphorus-covered dogs -- and says, "to hell with that."
and if you take what she is at face value, if you say she has magic powers and is a Mystery, a lot of the issues are resolved!
she shoots john with a tranquilizer gun and runs off? It's okay, she's a Mystery. she can't be understood.
she brainwashes anyone, like, instantly? it's okay, she has magic powers. she can't be understood.
those powers don't work on john, despite him being with her for a long period of time deliberately trying to be vulnerable? it's okay, she's a Mystery. she chose not to use her magic powers on John. why? she can't be understood.
and a genre switch can be done well. it would be difficult to pull off here -- a central tenet of mysteries is that there will be no Mysteries. but it can be done! unfortunately, moffat (and gatiss but this feels more moffat-y tbh and also i like him less so: moffat) seemed to believe that being an old white guy made his stories necessarily perfect, and character development and plot and coherency can go down in the mysterious well (it's okay, she has magic powers to erase wells from everyone's memories and, presumably, make victor trevor's parents forget they ever had a child) with victor trevor.
(and also, eurus's magic powers and Mystery don't even resolve everything, necessarily! where's rosie in all of this? who knows! eurus arranged for babysitting or something. how does john get unchained considering how fast the water's going up? i guess her powers extend to levitating other people also! i think it was @plaidadder who got caught up in the issue of the body of the therapist she was impersonating and how that worked so i guess she can. like. magically preserve people or mess with their [and animals'] sense of smell now!)
