Earlier quoted context omitted.
Less complicated systems successfully reason about more complicated systems all the time. Ditto for self-reasoning. See: bootloaders, update systems, and package managers. In order to prove that some kind of meta-cognition is inherently beyond our grasp, you don't just have to prove that the system we are attempting to reason about is more complex than ourselves, you also have to prove that the problem isn't meaningf…
I think you're describing an analogue of turing-completeness. It's not (to me) a question of whether we can reason about something: it's a question of how long it takes, and how much knowledge is involved with the process. What you're describing sounds like asking a PDP-11 to run GPT-3. Technically possible, in the broadest sense of the word. But a computer that can run GPT-3 successfully will look at that PDP-11 in…
In order for a problem to forever remain in "let's throw our arms in the air like it's an infomercial" territory, it must not merely be difficult in its most pedantically defined complete form, it also must stymie the search for useful relaxations and workarounds. Nobody fears running a program on account of being unable to prove that it will halt: they just kill the program if it locks up, or (equivalently) set a timeout. Personally, I'd just avoid throwing my arms in the air like an infomercial altogether.
EDIT: substituted GPT3 -> Windows because arguments about GPT-3 and/or a set of incarnations being Turing Complete would be irrelevant to the main point.