Why can't Mormon women hold the priesthood?
First, not everyone believes that Mormon women lack the priesthood power. So the conclusion that "women don't get to" may not be true. There are women inside the church who believe that temple-attending LDS women can hold a form of priesthood power, though this point has not yet been clarified through official channels.
Here is another general remark on the topic.
From Mormon.org, quoting Gordon B. Hinckley, former President of the Church:
“Women do not hold the priesthood because the Lord has put it that way. It is part of His program. Women have a very prominent place in this Church. Men hold the priesthood offices of the Church. But women have a tremendous place in this Church. They have their own organization. It was started in 1842 by the Prophet Joseph Smith, called the Relief Society, because its initial purpose was to administer help to those in need. It has grown to be, I think, the largest women’s organization in the world... They have their own offices, their own presidency, their own board. That reaches down to the smallest unit of the Church everywhere in the world...
“The men hold the priesthood, yes. But my wife is my companion. In this Church the man neither walks ahead of his wife nor behind his wife but at her side. They are co-equals in this life in a great enterprise.”
Priesthood "powers" do not make men superior in any way to women.
Some women may wish they could become a bishop, or a stake president, or hear confessions of sins. While that isn't possible in the LDS church, women have an extraordinary role to play, and they can have the gift of healing, see visions, speak in tongues, perform miracles, prophesy, protect their families, serve as missionaries, and more.
I think it is enlightening to understand that "women wanting the priesthood" means that these women do share core beliefs with their fellow Mormons. Unsurprisingly, the media and many anti-LDS Christian ministries ignore that pertinent fact. Some of them would seem to prefer that these women just become unhappy and leave the church. But that's not happening in significant numbers. So: What does this situation really say about the church, its doctrine, and its members?