It's a risk for sure but I'm riding on the presumption that there's going to be a plot twist, and that FL actually ISN'T the murderer. I know she gets arrested at the beginning but I think what will happen is she either gets framed or takes the fall for this murder, and the detective will be the one to try to prove her innocence in the end?
The author could've just kept this as a simple cat and mouse chase between the detective and FL, wherein he solves the murder and arrests her in the end. But adding in the "I've got a dead wife and FL reminds me of her" just adds a deeper and personal element to this, especially on the detective's end. There's still possibility that this all means nothing in the end but then why would the author write this element in?
I'm really just speculating and seeing where the story will go from here
Sure, but I'm a little skeptical to take this "confirmation" from the ML at face value. There's a reason why the author isn't just showing us what exactly went down and I feel that, it's because FL actually didn't murder him. I think at best, FL was probably a witness to the murder which is why she's acting so jittery.
Ch. 89 reveals that Jaeyoon is the son of a politician. I'm thinking that his own father probably found out what Jaeyoon had been up to (ie. hidden cameras, drugs, etc.) and had him killed. As the chief pointed out, politicians show no mercy even toward their own kids, if they get in the way of their future. Father probably had plans to run for a higher position and given Jaeyoon's criminal acts, killed him to eliminate any risks the father will get from losing his position.
I think that the ML speculating that FL is the murderer, will do more damage to their relationship. And will show that FL will truly have no one in her corner. The detective will end up being her only solace, to prove her innocence.
But again, she could very well be the murderer LOL I'm pretty much just coming up with theories here because I'm bored and too invested in this story lol

This is the second time that FL and detective have gotten in close proximity with each other The author is definitely setting something up between the two. Given the ring on his finger and him pondering if he's met the FL before, she likely reminds him of his wife? Just not sure if his wife is still alive or not ..
I'm thinking the detective will get closer with FL and possibly develops some affection or some sense of nostalgia(?) for her because of memories of his wife? FL will get framed for the murder, gets arrested but detective will be the one who will try to prove her innocence.