I don't see why you're "amazed". Neural networks are _provably_ an universal approximator. As such, they can approximate _any_ function to an arbitrary degree of precision. It just might require an impractically large/complex neural net to do so, and you might not be able to train it yet, but it's _provably_ doable in the limit, if you remove size/training constraints.
I'm a practitioner in the field, and an AI skeptic because of it. I think perceptual tasks work reasonably well, NLP barely works for anything, and any sort of cognition doesn't work at all, as of August 2020. I will be the first to admit that we don't have real "AI" yet, and we won't have it in the foreseeable future. But to say that real intelligence is not possible with the current tool set is simply incorrect. It may be impractical. It may take 100+ years to figure out how to build nets this large and train them successfully before sun burns out, but it is _theoretically_ provably doable.
In a way it's kind of like fusion: you have a proof that it can work right above your head during the day. We just don't know how to do it at our "human" scale with our knowledge and capabilities. Our knowledge and capabilities, however, are not a constant - they improve exponentially over time, although most people don't perceive this process as exponential.