Even if we ignore the massive complexity problems with whole-program analysis, what if you can't globally prove how the pointer is used? Pointer arithmetic can be done based on runtime information. A compiler doesn't have access to knowledge like 'this system will never encounter data that causes those pointers to alias'. If you add a system to provide information like that, well, you're pretty much defining a language extension right there.

Now, obviously you'd hope that people aim not to write programs that rely so subtly hopes and dreams of runtime information, but hopefully it's illustrative as a counterexample.