I believe you are closer on the latter. Look at John. He wasn't emulating Eurus subconsiously when he distanced himself emotionally from others, especially Sherlock. When humans get hurt, they have a tenancy to retreat. To isolate themselves emotionally to prevent further trauma. It's the same as jerking your hand away from a stove when you get burned. You try to avoid that which hurt you in the first place. Don't love. Don't feel. Be detached from your emotions.
That will keep you safe.
Of course it does the opposite. It leaves you alone - and miserable. That is Eurus' state - and John's state after Mary's death. You need the love of others to save you. And, as John provided that love to him and saved Sherlock, so Sherlock provided that love to John, and saved him. And, as Eurus needed that same love, so Sherlock finally provided it to her, and thus saved her as well.
I agree with this assessment on the love in the show. The love has been there since the very first episode of the show. It's a bit of a shame that John was reduced to a bit of a hanger on in this episode when the love that he represented un(sher)locked the mystery of the whole season. Love, love - always love.