In addition to what the others have already said above, there's no actual need for a full fledged story imo. Despite Oni stating he was going to make
"a fully formed dating sim with a full story mode" I doubt it's going to be easy to implement a story mode to what there already is. Well, he may add some events that expand on girls' story for example. And as
leathermax said:
You can make your own simulation of a story in your own imagination.
What this game needs is more variety; the game already has 6 girls and there are more to come I guess, but having more events, more locations, more dating options, etc. would be amazing. We did get a pool location not so long ago, but it didn't add much for me. Yes, you can sunbathe, swim and skinnydip, but these are very small events where you can undress the girls and lose a quarter of in-game time. It also added swimwear for the girls and that's about it.
So adding more variety can help expand the game's already great replayability. The problem right now is that the game may start to bore its old players. As for me, I know almost every single line of dialogue there is, I know what to do and what to say for certain meters to increase, I can bang and take control of all the girls in 10 to 20 days, so on and so forth.
And adding a full story mode would probably change the game entirely. Or it сould be easier to make a new game with a story mode
(for example, Four Elements Trainer), not a dating sim which it already is.