The purpose of Iddah for a woman of child bearing age is to determine if she is pregnant or not. What are the reasons behind observing same period for women who are well past their child bearing age (post menopause) ?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Iddah is a period defined by Sharia and the Muslimah must abide by it. Ibn al-Qayyim stated many wisdoms behind the Iddah, he said: "Among the wisdoms of the Iddah we have first to make sure that the divorced woman is not pregnant as to avoid mixing up progeny as this results in much depravity. Also, Iddah implies that the marriage contract is very sensitive and important. It also shows the high status of this contract and its great honor. In addition, Iddah gives man a relatively long period, so he can feel some remorse and decide to return to married life with his former wife.
Morever, Iddah is a period that gives the woman a chance to appreciate her husband's importance and his effect on her as she is not permitted to beautify herself during this period. Allah made the mourning period on the deceased husband longer than that on a brother or a father.
Finally, Iddah gives the spouse time to fulfill the rights of the husband, those of the women and of her children as well as abiding by the orders of Allah."
Allah knows best