I think this is a great line of research as it may solve the reasoning portion of AGI. The difficulty is that you would want to prove equivalence. LLMs can output stuff but for programs to execute you need to output correct stuff.
Most of the work I have read in this field is focused on finding potential malware or stolen copyrighted code, so false positives are no big deal. But you don't want anything less than 100% valid code coming out of your compiler.