You answered yourself : this is pron with a story, not the other way around. The cops and stuff are a means to the end, not the end itself. It then doesn't need to make any sense and/or work like the real life counterpart. Go to the VNs and such if you want a story that can hold itself with some lewds sprinkled around. You won't get that anywhere in here
The thing is though, the developers of TGO clearly put a lot of effort into the story. Lots of characters, dialogue, events, twists and turns. The bar for storytelling in these games is pretty low, and NLT do a better job than 90% of games on this site. There's a genuine attempt to tell a story here across multiple games. So when things don't seem right it sticks out. And it's not like I'm expecting a realistic police procedural here. Having cops act like cops shouldn't be all that hard to get right. It's more of a trend of developers for these games not seeming to understand how things in real life work.
Like all these games set in a "universitiy/college" but students have assigned seating, homework, and get detention. Anyone who's actually been to a university, or hell even seen one in a movie, will know that's not how universities work (and yeah, I know some games substitute "college" for "high school" to get around potential age issues - that's not what I'm talking about). If you tell me the characters are attending a university, but everyone behaves like they're still sixteen I find it jarring. Or when a dev's idea of an grown-up job is having a character go to the office to "work on the files" (because goddamnit, files need to be
worked). It's like the majority of these games are written by Vincent Adultman.