Okay, so I've been trawling through AO3 tags for 'Eve Polastri' for ages now, and something I notice a lot is how many writers kind of... skip the detective work? A whole chunk of post-canon fics basically have her quit the whole thing to go live in a cottage or run off with Villanelle, which is fun wish-fulfillment but feels disconnected from her character core. The detective challenges that do pop up tend to be more internal puzzles—like, 'can she outsmart her own obsession?'—rather than external crime-solving.
When they do tackle actual cases, it's usually a vehicle to force proximity with V. The mystery itself is just a MacGuffin, a reason for them to be in the same room trading that intense, creepy-flirty banter. The 'challenge' isn't the intellectual deduction; it's the emotional risk of the interaction. Which, fair, that's the heart of the show, but I miss fics that let Eve be clever in her own right, not just clever as a reaction to Villanelle's provocations.
I read one recently where she was investigating a copycat killer and the procedural details were so sharp, you could feel her frustration with bureaucratic red tape and her hyper-focus on tiny evidence inconsistencies. That felt true. Most others, though, treat her job as set dressing.