In the axiomatic system implied by the standard, the hypothetical compiler being discussed can prove that the null check can be eliminated. The fact that you believe this axiomatic system is inconvenient does not constitute a refutation of the truth of the theorem.

> If the compiler is unable to prove a transformation preserves correctness, it should not do the transformation.

Actually, the compiler is able to prove the invariance of correctness. Eliminating a null check after a pointer has been dereferenced does in fact preserve the correctness. Either the function is never called with NULL, and the program is correct, or the function is sometimes called with NULL, and the program is incorrect.

> the bureaucratic mindset holds that the rules are always, by definition, correct

Since you think that the compiler following the standard rigorously is "bureaucratic" and, I imagine, bad, it follows that you would prefer the compiler to sometimes ignore what the standard says and do something different. I suggest that you try compiling your code with a compiler for a different language. Compilers for languages other than C are guaranteed to not follow the C standard.

EDIT: I think I see where you're going. Your argument is that, since in some platforms NULL can be correctly dereferenced, if the compiler was to eliminate the null check, that would change the behavior of the program. If a compiler for that platform did that, I would agree that it would not be preserving correctness. A compiler for a given platform is only required to generate correct code for that particular platform. Compilers for platforms where dereferencing a null pointer is always invalid can correctly eliminate that late null check.