I just about always use it (Gray Flannel) after a wet shave. Not only does it soothe the skin, put it also helps to close up the pores which otherwise would remain more open after the shaving itself without it (or, more than just cool water alone could do). Which, can help to prevent new acne by closing them up before the bacteria can settle in. I personally notice my acne was worse after shaving before I started using it, and better after I did use it.
Also, another use of it I can think of for the aftershaves containing alcohol is as a disinfectant after a nick or cut, and even useful if you don't get either of those because you're still scraping off a layer of skin either way.
And, it's cologne too of course.
But yeah, you don't need to use it if you don't want too, especially if you're not using a blade against your skin. I know plenty who don't use it. But I prefer too because for me, it does make a difference.
I also follow that up with a small amount of extra virgin olive oil to moisturize my skin though. Give it a reprieve from the alcohol. Contrary to popular opinion, it does NOT block the pores and works a hell of a lot better than lotions or other commercial crap.