BaalHabooze: The Artscroll Machzor gives a different answer to that. They say that after a day of fasting and Davening on Yom Kippur we realize how much left we really have to do.
I always thought that is was a special law by Yom Kippur. Even a Tzaddik Gammur says it quietly all year round. On Yom Kippur (Kol Hayom Mechaper) we are like Malachim every second of the day, so as long as it’s part of Yom Kippur we say it out loud. As soon as it’s no longer than holy day we are not like Malachim, regardless of what level each individual is on.