You also say that an AI would rapidly consume the whole of human knowledge. For me, the totality of human knowledge would become a mass of contradictory statements, with little to choose between them on a linguistic level.
There are, for me, profound philosophical issues with creating a mind that is "conscious" in the sense that an AGI is implied to be, as a purely symbolic logical construction. Language is the only tool we have for programming a mind, and yet the mind cannot be completely described in language, nor can language seem to properly encompass whatever the fundamental ontology of reality involves. I don't feel there will be a "free lunch" where we advance computer science to the point where we get an explosion of the kind AI1 designs a better AI2, which designs an even better AI3, and so on. This seems to have a perpetual motion feeling to it, rather than one of evolution. It isn't to say AGI is impossible, but I believe that like everything else in computer science it will have to be solved pragmatically, and realising this could be an extremely long way off.