Exponential search spaces are completely typical for NP problems.
Even many "P problems" have an exponential search space. For instance an n-digit number has exp(n) many potential divisors, but there is a polynomial-in-n-time algorithm to verify primality.
"Reverse engineer" is "there is a machine that seems to find needles in haystacks quickly. It has loops of copper wire, and plugs into a wall socket. Can you copy it and build another one?"
I admit that there are some "reverse-engineering" problems that are easy.
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.