It's true and I wasn't aware of it till I read your post. When you think that parents see you develop from infancy, how you develop your speech, your ideas, how you improve in your ways of expressing them, I think that children often feel like performers in front of them. Parents are also a very careful public in the sense that they notice everything, what the child can do now that he couldn't do before, and they (usually) don't hide their happiness and admiration when seeing a progress, which in its turn makes the child happy and more motivated to perform.
I think there is a difference between the intensity of speech between children/parents and adult lovers. My experience of intensity of speech between lovers is not the "trying to impress/performance" part, but more a kind of seeing oneself in the eyes of the beloved. The gaze that is interested makes you become interesting. The desire in the eyes makes you desirable, it's another kind of intensity than child/parent.