I like dance? I like dancing? There are other ways to express this that should be accepted, I think
Mie is not necessary but it is used for emphasis. Romance language have a tendency to repeat indirect object pronouns
Mulțumesc foarte frumos! Italian is the only other romance language I know and that one doesn't repeat indirect object pronouns as far as I'm aware!
Why is mie needed here? Would it not be sufficient to just say îmi place? I was under the impression that îmi shows that it is a reflexive action on oneself?
„Îmi” does show a reflexive action, and indeed „mie” is superfluous; it serves to provide emphasis though, so it is not incorrect to use. In actuality, this double reflexive construction is very common in native spoken Romanian, especially when paired with the verb „to like” - „a plăcea”, as is the case in the example sentence.