Is there any issue for men going to the mikva at night? The customary thing seems to be to go before davening in the morning, or in the afternoon on erev Shabbos or Yom Tov, or at dawn on leil Shavuos, etc. What about during actual nighttime?
I'm unaware of any halacha that prohibits men from going to the mikvah at night (other than Yom Kippur and Tisha B'av.) I've occasionally seen men do this in my neighborhood.
However, practically, in many neighborhoods that have one mikvah or even a few, most of these are used by women for their tahara that ends niddah. So, of course, not only can't men go when women are there, but they really shouldn't even be roaming or "loitering" anywhere near the mikvah at night when women are there.
Ideally, places have dedicated men's only mikva'ot so going at night to these poses no problem. I recommend that before you go at night, inquire about the mikvah's night usage.
Incidentally, I have heard of some places that send men to "dunk" in the keilim mikvah - the one that's used for utensils. Apparently, this occurs somewhat more frequently than I imagined. The keilim mikvah tends to be ice cold and, honestly, not only would I not want to dunk my body in the keilim mikvah but, I wouldn't want to dunk my kli in that mikvah afterwards. So, somewhat aside, but, perhaps, relevant - anyone that thinks of going to a "men's mikvah" should ask about this. It's not always obvious if you're unfamiliar with the mikvah setup of that place, and, unfortunately, many places aren't volunteering this info.
As stated by others -- primarily it's about giving the women their own space and time.
But furthermore -- the primary halachic grounding for men going to mikva today is the enactment of Ezra against studying Torah after a seminal emission without first going to mikvah. If someone followed that, it would make sense for them to go to mikvah in the morning, before studying Torah.
But supposing that a man (and his wife) were on a nocturnal schedule and thus he wakes up at 9pm and wants to study Torah now, then yes following this logic that would be the time to go to mikvah.