Good points, however your definition of intelligence is something most people will not agree with. A hand calculator is very good at calculation, much better than any human in the planet. Your definition says that it is intelligent with respect to the goals that it was designed for. That of course is a use of a word that majority of people will definitely disagree with.
AGI’s main problem is not that of definition. It’s main problem is that we are very far from having a way to implement it.
See post on usefulness and specialized intelligence: https://medium.com/intuitionmachine/businesses-need-artificial-specialist-intelligence-not-the-other-kind-b0c285c1586e