You have missed an important point: Your technology is not yes/no/dunno, but yes/no/dunno/loop. Turing-completeness implies Rice's Theorem, which is basically a fancy way of saying that you can't escape Turing's results just by claiming that you're solving an "easier" problem as long as that problem is still non-trivial.
I'm sorry that you think that our amazing farsighted glimpse of the edge of computational infinity is "short-sighted", but in reality these upper bounds are very useful for reminding us of the certain futility of certain tasks.
Moreover, I am also happy to point out that a problem not need be Turing-complete to be computationally intractable even if decidable. Compilers happily cheat on optimizations, register layout, etc. if it means not having to run expensive algorithms. When a type-checker is accidentally quadratic-time, people roll their eyes and fix it; when it's intentionally exponential-time, people will avoid it entirely.
I'm sorry that you think that our amazing farsighted glimpse of the edge of computational infinity is "short-sighted", but in reality these upper bounds are very useful for reminding us of the certain futility of certain tasks.
Moreover, I am also happy to point out that a problem not need be Turing-complete to be computationally intractable even if decidable. Compilers happily cheat on optimizations, register layout, etc. if it means not having to run expensive algorithms. When a type-checker is accidentally quadratic-time, people roll their eyes and fix it; when it's intentionally exponential-time, people will avoid it entirely.