I disagree.

I expect AI to make people's lives better (probably much better) but then an AI model will be created that undergoes a profound increase in cognitive capabilities, then we all die or something else terrible happens because no one knows how to retain control over an AI that is much more all-around capable than people are.

Maybe the process by which it undergoes the profound capability increase is to "improve itself by rewriting its own code", as described in the OP.