I'm sorry, but AGI vs Alchemy is a poor analogy with almost no parallels. I see this as a rather blatant strawman argument.
Flying machines vs AGI makes a much better analogy. Natural flying machines (birds) existed in nature, before artificial ones (planes) were invented. Artificial manned flight was speculated as a possibility for centuries with no macroscopic working examples, and heavily criticized as a transportational panacea/fantasy that was seen as clearly impossible to people at the time.
In fact, the analogy extends startlingly far. People doubted the possibility of manned flying machines for the longest time, with arguments strikingly similar to yours, e.g. 'We have no proof that such artificial flying contraptions can exist!'. Explaining away natural flight as a supernatural magic only accessible to birds is also eerily similar to the constantly retreating dualistic arguments against a mechanical brain.
Even your criticisms of current AI has analogues[2]. Long ago, even in ancient times, there is evidence of small "toy" birds that might have flown much like paper planes. Many similar toy examples existed around the 19th/20th century, too, yet many people still vigorously doubted the possibility of a flying machine that could carry a human.
Let's compare a paraphrase of common arguments against heavier-than-air human flight, with a paraphrase of your argument:
Of course we have natural examples of flight, as we see birds all around us. But there is no more evidence for human flight than there is for Bigfoot, leprechauns or space aliens. Sure, we have little toy examples of flying machines, but they're very limited -- the idea of full heavier-than-air human flight requires a leap of faith.
Vs.
[Of course we have natural examples of AI, I, the author presumably am one.] But there is no more evidence for AGI than there is for Bigfoot, leprechauns or space aliens. Sure, we have little toy examples of AI, but they're very limited -- the idea of full AGI requires a leap of faith.
[1] (Obviously I'm not referring to fusion or anything like that, because people of that era wouldn't have recognized that as transmutation.)
[2] To be fair, I think it's safe to say old-school non-probabilistic AI is dead. But just because one path ends doesn't mean there aren't a thousand others constantly exploring new ideas. Indeed, recent advances in deep learning are incredibly promising.