It's clearly possible. There's not going to be some effect that makes it so intelligence only appears if nobody is trying to make it happen.
What might be the case is that it is inhumanly difficult to create. We know evolution did it, but evolution doesn't think like a person. In principle, we could set up an evolutionary algorithm to create intelligence, but look how long that took the first time. It is also arguably highly unethical, considering the amount of pain that will invariably take place. And what you end up with isn't likely to be friendly.
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.