One, you can't just mix up the chemical and spray away. You have to spread the solution on the nut sedge leaf without getting any on the leaves of desirable perennials or annuals. The procedure for accomplishing this is called wicking, and it's tedious work. Generally it's done by painting the herbicide solution onto the leaves with a disposable paint brush, or patting it on with a sponge. Some people even put on heavy rubber gloves and outer cotton gloves, then use their fingers to apply it. The cotton acts as the sponge, and the rubber keeps the chemical off the skin.
The second drawback is that multiple herbicide applications are usually required. The leaf absorbs the chemical, converts it into a hormone during photosynthesis and sugar production, and sends some of it into the root for storage. Once in the root, this hormone is deadly. Yet the root system may be more extensive than the leaf surface at the time of herbicide application. In that case, since leaves can only produce the root-killing hormone in quantities equal to their size, only part of the root is killed and a second application is necessary.
The way we see it, if you do all the work to wick on a herbicide, and make a follow-up application three weeks or a month later, you won't save much time. Also, considering the price of herbicide, brush and gloves, you will have paid more for the same result.
It's often depressing to deal with weeds, and all of us wish for a magic wand though we know in our hearts that none exists. We have two favorite books that console us in such times. One isAll About Weeds, by Edwin Rollin Spencer (Dover Books, New York, 1968), and the other isWeedsby Walter Conrad Muenscher (Cornell University Press, Ithaca, New York, 1980). These books have taught us the true names and natures of weeds - valuable lessons, that fit with what we heard as kids, "It's more powerful to curse it by its right name."
Both books list various strategies for controlling specific weeds, and since the authors have actually "been in the field" - one as a farmer, the other as an extension service botanist - the advice is practical. Though we long for a magic wand, it's comforting to hear from those who've been battling weeds for much longer and in greater quantity than we have, that there is hope.