it is a well-known an widely accepted without much evidence idea that brain just can't be simulated by any sort of Turing machine.
Is it? I don't think I've ever encountered this view. I think the opposite view that the brain is approximated by a turing machine is widely voiced, e.g. Kurzweil.
You mean you've never met any non-transhumanophile and/or non-SF-bay human? (I kid, I kid.)
Walk down to your nearest non-SF-bay starbucks and ask the first person in a business suit if they think we could ever simulate brains on computers. Wager you on >4:1 odds that they'll say something that boils down to "Nope, impossible."
For starters, the majority of devout religious followers (which is, what, more than half the worldwide population? more than 80%?) apparently believe souls are necessary for human brains to work correctly. Or at least for...
If Strong AI turns out to not be possible, what are our best expectations today as to why?
I'm thinking of trying myself at writing a sci-fi story, do you think exploring this idea has positive utility? I'm not sure myself: it looks like the idea that intelligence explosion is a possibility could use more public exposure, as it is.
I wanted to include a popular meme image macro here, but decided against it. I can't help it: every time I think "what if", I think of this guy.