Goal-completeness doesn’t make much sense as a rigorous concept because of No-Free-Lunch theorems in optimisation. A goal is essentially a specification of a function to optimise, and all optimisation algorithms perform equally well (or rather poorly) when averaged across all functions.
There is no system that can take in an arbitrary goal specification (which is, say, a subset of the state space of the universe) and achieve that goal on average better than any other such system. My stupid random action generator is equally as bad as the superintelligence when averaged across all goals. Most goals are incredibly noisy, the ones that we care about form a tiny subset of the space of all goals, and any progress in AI we make is really about biasing our models to be good on the goals we care about.
If you’re thinking of “goals” as easily specified natural-language things, then I agree with you, but the point is that turing-completeness is a rigorously defined concept, and if you want to get the same level of rigour for “goal-completeness”, then most goals will be of the form “atom 1 is a location x, atom 2 is at location y, …” for all atoms in the universe. And when averaged across all such goals, literally just acting randomly performs as well as a human or a monkey trying their best to achieve the goal.