It is not authority that women want but power. People want power to change lives for the better and make a difference. But you don't need to have authority in the LDS Church to have power. You can have even more power in your local ward through influence than by authority.
I have had the calling of activities chair at a BYU singles ward. This calling has very little priesthood authority but very big influence. My roommate was the Elders Quorum Pres. He and the Bishop controlled what went on for 3 hours on Sunday. I controlled almost everything that happened the rest of the week. Through activities and regular service projects our singles ward had near 40 marriages the following summer (myself included). I felt very powerful and influential in this calling.
I didn't need Church priesthood authority (pay the bills and take out the garbage) to have power in the LDS Church to make a difference. But acting under priesthood authority, I had great influence and power to help and bless others.
My wife has had similar power in a ward as Visiting Teaching Coordinator. She had had great power and influence in the ward with that calling because she makes a point of visiting and knowing everyone. The bishop has her on speed-dial when she has had that calling.
You can "minister" in the LDS Church without having to bother with the "administering". God knows women are way better at ministering so he doesn't waste their talents on the paperwork.