In the Bokuto Ni Yoru Kendo Kihon Waza Keiko Ho (Kihon Kata, for short), kote-men is the second kata performed, and is used to illustrate renzoku waza (continuous attacks). I believe there is a very good reason that kote-men was chosen to exemplify this. I may be wrong. It wouldn't be the first time, nor will it be the last. In my experience, though, kote-men is not only a useful technique in and of itself, but it's a very versatile technique and can be used in a whole range of different situations. Obviously in order to use it effectively you have to have a solid grasp of the individual attacks of kote and men, but with that part under your belt you can begin to use it to learn about continuous attacks, multiple strikes, and stringing together other attacks into useful techniques.
Kote-men does a lot to teach us about the rhythm and flow between attacks necessary to combine other attacks. Want to strike men a few times in a row to catch your opponent off guard? This technique can help with that timing. How about kote-do? Yup, this can help, too. So, looking past just the specific attacks themselves and digging in a little can give us a framework that we can apply to create almost any combination of attacks that we can think of. We can use big strikes mixed with small strikes, as well, or different timings to create surprising and unexpected rhythms for our opponents to deal with. Like I said, versatile!
Kote-men also doesn't have to be applied to just strike the kote and the men targets. It can be used as a great way to create an opening. Simply bringing the shinai down the midline, as if you were attacking kote, can open the center for you, and give you a nice, direct path to the men. It can be used to attack either omote or ura side of the shinai for openings, as well. It can also be used with off-timing to open and then attack as the opponent regains the center and, possibly, overreacts to try and block the men. At this point kote, do, or even tsuki open up for attack. Once you have the basics of the technique down it's good to experiment and explore the options that are available to you.
We can use this technique as not only attack, but defense. Kote-men is a great way to counter and open an opponent that's moving to hit your own kote. Just a quick strike down the center as they move in, shinai-to-shinai, is enough to throw a lot of people off target and open their men for a counter attack. We can also see this motion in Kihon Kata 9 (uchiotoshi waza), where it is used to divert an incoming do strike. I don't know how many times I've used this myself; just a quick strike to the shinai as it comes in to open my opponent up and, depending on how they react or not, I'm presented with different sets of opportunities to take advantage of.
This is just a taste of the many, many uses of this waza, and the benefits that it presents. I'd encourage anyone and everyone to take a serious look at it and see what they can use in their own kendo. Whether you're using kote-men as is, or using the timing to build new renzoku waza that you like, or if you're utilizing it for new defense and counter techniques, kote-men is a versatile and useful waza to learn.