If you're gonna look at it that way, then the halting problem is just a dressed up computer science version of the question "can God make a rock so heavy even he can't lift it?" Could an infinitely smart AGI come up with the answer to the unanswerable question?
It doesn't need to be infinitely smart to do a better job than the worst of humanity's blunders.
But isn't on the other hand the current AGI problem posed similar to the question "Are you not afraid that genetic engineers grow babies with bigger and bigger brains?"
We don't know if that won't break down somewhere. Looking at different examples it probably will. Scaling things infinitely is a pure math only concept it seems.
How would it make the combinatorial explosion in state space search go away, to pick one example?
And if it doesn't, is it then an infinitely smart AGI?
The concept seems to assume all problems humans struggle with can be solved. The halting problem is one witness that this is probably not true.