Brilliant. Anyone familiar with the halting problem ought to be sold after the first two paragraphs.
Totally get where you're coming from! The whole AGI thing is super complex, and it's easy to get frustrated when it hits so many roadblocks. Current approaches might seem like they always "halt," but think of it like science in general: we've gotta stumble and fall a lot before we figure out how to run smoothly. Even the best minds are constantly learning and refining their methods, and it's pretty amazing how far we've come already. Just imagine how AGI will look in a few decades! Maybe not perfect yet, but each halt is a step closer to something truly groundbreaking.
I generally agree, while there is a lot of hype around AI, there is real progress being made as well. The way I see it there are three different paths towards AGI. The first is trying to figure out the algorithms similar kind of problem solving that our brains are doing. This is the approach that's getting the most attention currently. Another approach is bio-inspired neural nets, where we study how biological systems evolved, and try to copy that. Finally, there's the evolutionary approach where we could set up a virtual environment, and have the agents evolve within it. We can also use combinations of these techniques in complementary ways.
I'm convinced that we will stumble on what's involved in building human style intelligence sooner or later, but it's hard to say how far away we are at the moment. I do think that this will happen within a century tops though, and even that is a blink of an eye in the grand scheme of things.