Why does moving a pointer variable not set it to null?

Setting a raw pointer to null after moving it implies that the pointer represents ownership. However, lots of pointers are used to represent relationships. Moreover, for a long time it is recommended that ownership relations are represented differently than using a raw pointer. For example, the ownership relation you are referring to is represented by std::unique_ptr<T>. If you want the implicitly generated move operations take care of your ownership all you need to do is to use members which actually represent (and implement) the desired ownership behavior.

Also, the behavior of the generated move operations is consistent with what was done with the copy operations: they also don't make any ownership assumptions and don't do e.g. a deep copy if a pointer is copied. If you want this to happen you also need to create a suitable class encoding the relevant semantics.

I think the answer is : implementing such a behavior yourself is pretty much trivial and hence the Standard didn't feel any need to impose any rule on the compiler itself. The C++ language is huge and not everything can be imagined before its use. Take for example, C++'s template. It was not first designed to be used the way it is used today (i.e it's metaprogramming capability). So I think, the Standard just gives the freedom, and didn't make any specific rule for std::move(other.p), following one of it's the design-principle: "You don't pay for what you don't use".

Although, std::unique_ptr is movable, though not copyable. So if you want pointer-semantic which is movable and copyable both, then here is one trivial implementation:

template<typename T>
struct movable_ptr
{
    T *pointer;
    movable_ptr(T *ptr=0) : pointer(ptr) {} 
    movable_ptr<T>& operator=(T *ptr) { pointer = ptr; return *this; }
    movable_ptr(movable_ptr<T> && other) 
    {
        pointer = other.pointer;
        other.pointer = 0;
    }
    movable_ptr<T>& operator=(movable_ptr<T> && other) 
    {
        pointer = other.pointer;
        other.pointer = 0;
        return *this;
    } 
    T* operator->() const { return pointer; }
    T& operator*() const { return *pointer; }

    movable_ptr(movable_ptr<T> const & other) = default;
    movable_ptr<T> & operator=(movable_ptr<T> const & other) = default;
};

Now you can write classes, without writing your own move-semantics:

struct T
{
   movable_ptr<A> aptr;
   movable_ptr<B> bptr;
   //...

   //and now you could simply say
   T(T&&) = default; 
   T& operator=(T&&) = default; 
};

Note that you still have to write copy-semantics and the destructor, as movable_ptr is not smart pointer.

Moving renders the moved-from object "invalid". It does not automatically set it to a safe "empty" state. In accordance with C++'s long-standing principle of "don't pay for what you don't use", that's your job if you want it.