Agree :) To be fair, most of these AVNs aren't really "games" as they are visual novels to begin with :) Many which have "choices" mostly have pseudo-choices which only have minor influence on the story. Having many different outcomes would just multiply the work and reduce the length of the story.
I'm also here mostly for the stories. What's great about Cosy Cafe is, that it's one of the most believable story in the AVN pool (besides the fact that all girls are ok with the whole polyamory thing. Though the founding family setting is actually a great excuse ^^).
I recently finally gave Eternum a shot after many people praising it. It of course depends on your preferences, but Eternum is, hands down, one of the best stories out there. Top graphics, brilliant and diverse character design (visual and personality) and an incredible soundtrack. For Eternum I changed the meaning of AVN to "Audio Visul Novel". It has 250+ music tracks (you can find a playlist on YT by user "dead" ( @DeadBrokenMind ). I'm always quite sceptical when people recommend things, those deserve their praise ^^. Story wise it touches almost every genre. It could be summarized by Ready Player One, Matrix, Ocean's 11 and Pirates of the Caribean :P Though that doesn't even capture it all.