"– Are you ready? – I am."
Translation:– Oletko sinä valmis? – Olen.
Yes. If you notice, all of the questions with "on" as answer, had the question starting with "onko" (now you see where the "on" comes from), plus the adessive form of a pronoun (sinulla, hänellä, etc). Since "valmis" is an adjective which one can't feel (like cold, hot, hunger, thirst...), the pronoun will be in the nominative form (Minä olen valmis), so the question will be (Oletko valmis?). Thus, you have the answer with "olen" instead of "on"
I think that you might be refering to phrases like "Minulla on kylmä" (I am cold)? I think it's a case of literal translation and a more correct translation clashing. As far as I can tell (and please do correct me if I am wrong since I am a novice at this language) cold is something you have, and not something you are in Finnish.