in other contexts, 'person' is allowed as a translation for 'człowiek' - why not here?
Well, it's not exactly an equivalent. Deciding on when it works and when not is often hard for us.
I'd say it like that: "Jesteś człowiekiem!" either is a super Captain-Obvious thing to say, or it sounds like from science-fiction/fantasy. And while Spock or Elrond definitely are persons, they are not human.
"You are a person" definitely works in English here! "You are a human" is an odd thing to say in any context but a science fiction story. "You are a person" could be used in other contexts. Eg "you are a person so you deserve respect".
(Nice to see you admitting Spock is a person, though )
What happens when you do not accept 'person' here is that you drive us to answer 'human' everywhere, otherwise we generate random rejections. If the question has no way for the beginner to predict the answer, it has no place here.
"human" without an article would be an adjective, whereas "a human" is a noun. So since "człowiekiem" is a noun it should be translated as "a human".
"You are human" would be something like "Jesteś człowieczy". I hope that helps.