I think they're just used to unlock content. It's so that the game "knows" if you can have certain events with the girls. For instance in the last update in a "Katherine only" playthrough I didn't even get the option to go to the cinema with Sarah and when I met Rose at the bar I didn't get her text and the scene that follows.how does the point system work do they matter or not seems its just a tracker to whichever person you spend more/less time with but no consequences?
As for the consequences, from Dev Notes:
Cheating tag – you’re the one who has the option to cheat or not. It’s NOT used as a punish mechanism for people who want to explore other routes as well. There may be some consequences if you choose the dark side (to test your villainy), but nothing involving third parties.
So I don't think that the points you have with each girl really matter. It's the good guy/bad guy points that might have consequences.