and let's assume, for the sake of discussion, that we don't run into any fundamental limitations

We already know there are massive fundamental limitations. All of the big name AI companies are all in on LLMs which can't do anything that hasn't been done before, unless it is just arbitrarily outputting something randomly mashed together which is not what to do for anything important. It is a dead end without humans doing things it can copy. When a new coding language is developed, it can't use it until lots and lots of people have used it to suck up their code to vomit forth.

LLMs, which is what all of the general purpose AIs are, cannot be a long term solution to anything unless we are just pausing technology and society to whenever it can handle 'everything'. LLMs have already peaked and that is supposedly the road to general AI.