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 just remembered reading a paper that said "moving should never be more expensive than copying" or something like that. Setting the original pointer null would break that rule. Do you know which paper I'm talking about, or did my brain make that up?
I'm not completely fine with the first sentence "Setting a raw pointer to null after moving it implies that the pointer represents ownership." Why is that? I disagree. In a modern code base heap ownership is handled by smart pointers. Raw pointers are merely equally to a reference, except that the developer has the option to reference to "nothing". In an old code base you do not know if a pointer is used for owning heap or just referencing something. Thus setting a pointer to null IMHO does not imply owning it.