I don't think I have a problem with that. Although times do change, and women don't do it often now. When going through hardships or trials I can see how a woman would give a blessing to someone sick, it is all by the hand of god.
I remember hearing somewhere something about kings and queens, priests and priestesses. We don't know everything and we don't know what lies in the future.
Remember that even though we don't practice polygamy any more it is still a gospel principle.
I remember reading an old church manual, from the seventies I think, and it said that mothers could give blessing to their children but, it was through faith and not through the Priesthood. It did not say anything about women using olive oil though. I don't believe the modern home and family manual says anything about women giving blessings.
Here is the PDF: A Gift Given A Gift Taken.
This is an interesting article on the subject, I wish I could find the old home and family manual that I quoted.
When a woman has her calling and election made sure, he is anointed a Queen and a Priestess. What is a Priestess if not a woman who holds priesthood? However, I think that it is Patriarchal Priesthood which she holds with her husband, which gives her authority to preside over her own posterity forever. It is not the temporary priesthood that men hold today, which gives them authority to preside over those who are not their posterity, and which authority they will not hold in eternity.
Unless a woman has her calling and election made sure, then whatever blessings she might give would be essentially a prayer of faith, as Heber C. Kimball indicated, and would not be done by the power of the priesthood which she does not hold.
My sister lives in the country side where home teachers cannot always be there every month, she is a single mother of 4 kids so because we study together LDS doctrine and history she was very glad to read about the experiences of the early sisters with regards to healing so she does that with her own kids when the home teachers aren't around.