An independent woman doesn't necessarily annoy the brethren if she's independently following the gospel path. It's the women (no matter what adjective you lead with) who won't conform to the mormon mold, who think for themselves, and who won't kiss the priesthood's butt.
Next thing you know, some woman's gonna say she got a revelation!
As long as the revelations don't challenge The Brethren (TM), they love it. See: Ruby Franke and Lori Vallow. And we all know how well that turned out!
It's about control. The younger members pretty much ignore the church leadership anyways. The ones who stay in it pretty much stay because there is a benefit of some sort but they stay in on their own terms. It will be interesting to see where the church is in another 30 years. It won't be like it is now.