"I like mint."
There are two types of adjectives;
い adjectives that end in い are able to conjugate like verbs and do not require a copula to be a complete sentence. (高い、小さい、etc.)
な adjectives are adjectives that require a な to connect directly to a noun and cannot conjugate on their own so must be used with a copula.
Despite how it sounds, 好き is a な adjective and requires です or informally だ to be a complete sentence.
It depends very much on the context. Usually when you tell somebody which your favourite is, there are supposed to be a few or more choices. In this example mint is one of them. Until you specifically mention mint, it is still just one of the choices, not a main topic. Using が actually distinguishes mint from the other choices. The hidden topic is "Me".
(As for me,) mint (rather than other flavours) is desirable.
Of course if mint has become a topic already, e.g. the previous sentence is a suggestion to buy mint flavor ice-cream, then your sentence would fit.
I read on another of these discussions that が is used to emphasize new information https://forum.duolingo.com/comment/32541058?comment_id=35420087 I don't think that makes sense here. So I'm wondering what function が does have here? And what functions can it have?