Most of the use of mathematical theorems are not from their results, but from the insights obtained in the way of reaching that result. Accepting the Halting Pr

Most of the use of mathematical theorems are not from their results, but from the insights obtained in the way of reaching that result. Accepting the Halting Problem as a proof of the incompleteness theorem misses out on all of them. Suppose that I hacked the Turing Machine to always respond `true` to the halting problem. Now nothing is undecidable. What is wrong with this action?