Of course your compiler will never be able to proof the correctness (or lack of it) of all programs.
The relevant question is, what share of useful programs can our compilers help us creating? This is not answered yet, and you seem to have never even thought about it.
fun fact: the Busy Beaver function applied to the universe yields a finite number and seeing as we need to leave some space to actually run the program we can conclude that in fact any program that can be written can be proven to halt. Granted that in case of "for(;;){printf("hello");}" that halt is the heat death of the universe but it's still theoretically tractable.
Of course your compiler will never be able to proof the correctness (or lack of it) of all programs.
The relevant question is, what share of useful programs can our compilers help us creating? This is not answered yet, and you seem to have never even thought about it.