I don’t think you understand what a doula does and what their purpose is. You are drastically reducing her value to a gopher (go for ice, go for hand holding, etc.), which is
not what they are and it is incredibly disrespectful. A doula is a third-party person who speaks on behalf of the mother
and the father. It has little to do with how comfortable/confident the mother or father is. You may be positive that you can handle everything a doula does, but, when push comes to shove, you really have no idea how you will deal with until it has already happened. She knows how she would handle it because she’s done it before. The idea is to have that support and help in advance, even if you may not need it. Remember, once you’re in the delivery room, you can’t change your mind.
Think of it like an attorney. They give you advice, encouragement, help, support, and will speak up on your behalf the instant things may go sour, without holding back. They can document everything through written and photo record, while you may be too busy or preoccupied to do so. They are well educated and have gone through rigorous training to help you. They represent you, not the other party and have nothing to lose by standing up for you. Think of a courtroom. Would you rather have an educated, experienced attorney representing you or would you rather try to represent yourself?
Here is a really good description of what doulas do:
childbirthsolutions.com/articles/birth/doula/index.php
Here is a really good quote from that site, which I think addresses your concerns here:
Sometimes a father may feel uncomfortable with hiring a doula, fearing that she will take over his role in the process. Doulas provide an atmosphere of safety and comfort, as much for the woman’s partner as for the woman herself. With a doula present, the pressure on the father is decreased and he can participate at his own comfort level. Fathers often feel relieved when they can rely on the doula for help; they enjoy the experience more.
That said, I have never met a mother who regretted hiring a doula. If they didn’t use one on a previous birth, but used one on a later one, they have always said they wished they knew about them before or hired one then. Everyone who has used them once will use them every time after. I have not had a child yet, but I already have the doula directory in my area bookmarked.
If this doesn’t convince you to let your wife hire one if she wants to, maybe the statistics will:
childbirth.org/articles/stats.html