This all sounds like the stochastic parrot fallacy. Total determinism is not the goal, and it not a prerequisite for general intelligence. As you allude to above, humans are also not fully deterministic. I don't see what hard theoretical barriers you've presented toward AGI or future ASI.

I haven't heard the stochastic parrot fallacy (though I have heard the phrase before). I also don't believe there are hard theoretical barriers. All I believe is that what we have right now is not enough yet. (I also believe autoregressive models may not be capable of AGI.)