Something I hope Smilingeyes hasn't written about.

If

conscious is "I focus on it."
unconscious is "I ignore it."

and

strong is "I can do it."
weak is "I can't do it."

Then,

Ego is "I focus on something I can do."
Super-ego is "I focus on something I can't do."
Super-id is "I ignore something I can't do."
Id is "I ignore something I can do."

So,

valued is "I focus on something I can do or I ignore something I can't do."
non-valued is "I focus on something I can't do or I ignore something I can do."

(See also http://socionics.us/philosophy/differentiation.shtml)

From this it is obvious how the valued-nonvalued functional dichotomy (i.e. quadra values) results. In a perfect world we could focus on our strengths and ignore our weaknesses. Thus the Id is intentionally subdued because it is unconscious and strong, and the Super-ego because it is conscious and weak.

QED.