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It cannot be assigned as penance. Its purpose is not to get the sin absolved, but to shorten the stay in Purgatory.

I'm not sure what you mean that an indulgence cannot be assigned. Power of indulgences rests with the Church-not the individual. From newadvent under Indulgences:

Once it is admitted that Christ left the Church the power to forgive sins (see PENANCE), the power of granting indulgences is logically inferred. Since the sacramental forgiveness of sin extends both to the guilt and to the eternal punishment, it plainly follows that the Church can also free the penitent from the lesser or temporal penalty. This becomes clearer, however, when we consider the amplitude of the power granted to Peter (Matthew 16:19): "I will give to thee the keys of the kingdom of heaven. And whatsoever thou shalt bind upon earth, it shall be bound also in heaven: and whatsoever thou shaft loose on earth, it shall be loosed also in heaven." (Cf. Matthew 18:18, where like power is conferred on all the Apostles.)

It certainly can be assigned by the Church. However, if you mean the Church states what makes up an indulgence and it's up to the Catholic to applied it to one's life than I would agree with you.

The passage from the Catholic Encyclopedia you cite says that the Chruch may grant indulgences. Sure she does; and an indulgence was just recently granted:

POPE: ALLOWS PLENARY INDULGENCE FOR 8 DEC
(AGI) - Vatican City, Italy 29 Nov - Benedict XVI has issued a plenary indulgence for 8 December, on the occasion of the 40th anniversary of the end of the Vatican Council II. A decree from the from the Penitenzieria Apostolica, signed by Cardinal James Francis Stafford, establishes that the concession, "the gift of the plenary indulgence, available on the usual conditions (sacramental confession, Eucharist confession and prayer in accordance with the intentions of the Supreme Pontiff) with the soul totally detached from the effect of any sin, in the solemnity of the Immaculate Conception by the faithful, if they take part in a sacred rite in its honour, or at least offer an open demonstration of devotion to the Virgin Mary in front of a statute or image of the Madonna Immacolata displayed for public worship, adding the Lord's prayer and the affirmation of belief and a prayer to Madonna Immacolata". The indulgence is to be allowed also to those faithful 'prevented by infirmity or for any other good reason, so that with the mind detached from every sin and with the intention of obeying the above conditions, as soon as they can, they unite in spirit and wish with the intention of the Supreme Pontiff in prayer to the Madonna Immacolata and recite the Lord's Prayer and the affirmation of belief. (AGI) -
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I said that an indulgence may not be assigned as penance in the course of a confession, because it has a different purpose.