I think you're stretching Gödel too far. Perhaps most "fundamentally", it speaks to a limitation on finite first-order logic systems, and "computer languages" g

I think you're stretching Gödel too far. Perhaps most "fundamentally", it speaks to a limitation on finite first-order logic systems, and "computer languages" generally don't impose a finiteness constraint (a language which does would not be Turing Complete). Though if I'm missing the point you're making, it would probably be quite interesting to see it in more depth.