What I infer from your example is a confirmation of the very reason which was behind my question. And my inference is that Mr. X arrived anywhere but here. So, when someone's whereabouts is not know (let's say, for 24hrs to be officially called "missing"), others don't know where they might be, thus where they may have arrived is out of question. Ok, I know that when someone gets Y(an unknown place) from X(the last seen place), yes ,they arrived Y, but I don't think people talk about the missing persons arriving places, people talk about where they are. But if you think what Tdol( a native-speaker) said sounds natural to you (also a native-speaker),
then my reasoning has some flaws, and I'd be happy if you show me where in my reasoning they may be.
I think the point is that there is a difference between being "missing", presumably fairly temporarily, as in my example, ie simply missing from where we knew they were fairly recently; and the more serious "missing" when it might become a police issue - someone has actually vanished and isn't in any of the places where you might expect to look for them. In that situation, I would be inclined to use "He's gone missing".
I've tried to come up with some conversational examples for the three sentences you gave:
Me: I thought John was coming to the party.
You: Yes, so did I.
Me: I haven't seen him. Have you?
You: No, I haven't seen him either.
Friend: Hi, you two, where's John?
Me: We were just talking about that. He's missing.
Friend: Oh well, maybe he'll come later.
Me: I just saw lots of police cars outside your house. What's going on?
You: Oh, it's my brother.
Me: What's happened?
You: He's gone missing. No-one's seen him since 7pm last night. We're really worried.
Me: Have they found your brother yet?
You: No.
Me: How long has it been now?
You: He's been missing for nine days.