To make it effective, you'd only want it to apply to GC pointers. But the type system does not distinguish between GC pointers and other pointers, making such a mode a rather complex implementation problem.
If you have a struct on the stack, and call member functions, you've got pointers. For an array on the stack, taking a slice of it or looping through it with pointers, you've got pointers. For a variable on the stack, passing it by ref to another function, there are pointers.