Makes the game more interesting... And I feel there are few games of that style for mention a few Unaware in the City (despite that doesn't have story) and one that has it is College Craze but damn... That game hasn't been updated in a while
The way I see it, most VN's are actually more or less kinetic with maybe two or three somewhat different paths and lot's of flavour choices (e.g. regarding side girls, or certain fetishes).
The amount of VN's which have really divergent paths based on your choices are (in my opinion) quite limited. Games by Eva Kiss come to mind.
I am fine with games having options, and even combat/minigames or whatever, the only thing I dislike is that you have to replay the game multiple times to see every route. I prefer where you can have every route in one playthrough but having different scene's for the routes i.e. dating 2 people instead of one. there's a chance of getting caught. something like how Love & Sex: Second Base. where when you are out on a date with love interest, there's a chance that another love interest will see you if they are at that location.
If you are doing a more linear story then you could have something like that in your game and have it cut off routes from both love interests or one of them.
Google "Choose Your Own Adventure." They were games in book form in the 80s. At the bottom of some pages would be like "If you choose to do A turn to page X, if you choose to do B turn to page Y."