It's a little more complicated. Sousuke himself is very stubborn and naive, so to find closure is most likely his reason. But mostly nails down to how even worse she is every time he finds something about her. As for going to the police, in the end, it'd be useless. Rika is in league with Iwabuchi, and as said by Kanebayashi, he's extremely difficult to legally approach by his position.The mangaka is making this story too long and it has lost much of its edge. It's not even clear why the heck Sousuke is chasing Rika. He has a daughter to raise and for all intends and purposes his relationship is dead. Closure is fine and dandy, but why would he pursue it? If the issue is the possibility that Rika is pregnant with his child, going to the Police would be more logical than all these events from the latest chapters.
Also, why are peeps applying ntr/hentai logic to the story? There isn't none. Even the most NTR situation right at the beginning solved itself when the teacher lost his influence: the mothers wanted to skin him alive for not being able to fulfil his promise of giving their kids an advantage in admission.
And, I will bet some hard cash that the confrontation most peeps are still reading this for, will be a whole handful of nothing. Rika will say something vague but deep sounding and leave them all behind...
There's no sheer NTR, only adultery. And even in Shiratori's case, NTR was acting. However, Sousuke DOES( until near the end of the spa arc) still get aroused by Rika, even if she's with another man. This has subsided since he started really falling for Akiba...but our overall main conjecture lies in the possibility that Rika KNOWS he idolized her, and believes he's still following through with it, so she continues to toy with him. Not aware that he already changed his perception.
It might be. They might clash their ideals as well. As we don't know how Rika's ultimate goal works, nor how she thinks or even her backstory, it may be a surprise, or something more direct( in a past point, we talked about how some of her characteristics reminisce those of psychopathy, so it might be just as direct as that).
In the end, the most important things are how far can Rika go in her plan, and how much longer will it take for Sousuke to realize that, although he preaches punishment to cheaters, he himself is showing clear signs of changes. From betrayal, detaching emotionally little by little, and now checking out.