If the purpose of Kaddish is to alleviate the judgment of the soul (the neshamah) — for which reason we cease saying Kaddish after 11 months — then why is it at all necessary to recite Kaddish after the passing of a great tzaddik, a righteous man or woman? It should be quite obvious that such souls have no problem with any heavenly judgment!

The answer for this dilemma may be found in the Kabbalistic writings of the Arizal (and in fact it is cited also in halachic sources).

As to the Kaddish which is recited during the first year...the reason is not as is commonly believed by the general population that it only helps to save the soul of the departed from the judgment of purgatory. There is another benefit (advantage), the Kaddish leads the soul into the Garden of Eden ("paradise") and it helps to raise the soul from level to level1.

It is for this reason that the Kaddish is also recited on Shabbos and Yom Tov during the eleven months. (Although all souls are relieved from the punishment of purgatory on Shabbos and Yom Tov we still say Kaddish to effect an ascent.)