Yea they do. Either the author never went to one or for plot convenience they don't have cameras...
Not all karaoke rooms have cameras in shinjuku. If you say no to going to a love hotel with a guy they often ask to go to karaoke instead. Like if a guy asks you to go do karaoke after a few drinks it's the shinjuku version of Netflix and chill
And not cleaning his butt first is also for plot convenience.
What if the security dude has a voyeurism kink?
Aren't they in a karaoke room!!! I'm not sure about Japan but here in America we have cameras all over the room! Lol I feel bad for the security dude