I recently came across a list on Letterboxd that interested me. It was about science-fiction films where the "sci-fi" element is not the main plot point of the film. I have linked this list below -- there are a lot of really good movies on it that you should check out.
I was really intruiged by this usage of "soft" too -- it's the perfect descriptor for films like Another Earth, Melancholia, and even Tarkovsky's Stalker which use the sci-fi element of their film more as a backdrop and less as an overt plot point.
Take Melancholia for instance. The film (as the opening minutes reveal) takes place right before the entire Earth is destroyed. In this way, it is a science-fiction film, concerned with the imminent destruction of the planet. However, the substance of the film is about depression -- mainly Justine's depression as she goes through the motions of her wedding day.
Lars von Trier uses the intriguing sci-fi element (the destruction of the planet) to tell a more powerful, human story. By doing this it not only elevates the genre itself, it also puts the human story in a fresh perspective. The planet is used as a metaphor, rather than just an overt plot device.
Take another film -- Spike Jonze's Her. In it Joaquin Phoenix's character is depressed and lonely. Then he gets Samantha -- a Siri like device which speaks with him. Eventually, he develops a relationship with this device. However, the story is not about the device itself, or its cognitive capabilities (though they are mentioned throughout the film); the story is about loneliness, attachment, human interaction, and depression. By putting it through a sci-fi lens, though, Jonze was able to take old themes and present them in an exciting way, making them feel fresh and original.
But "soft" sci-fi doesn't have to just reprise old ideas. Films like James Ward Byrkit's Coherence stand out as incredibly impressive independent efforts that use science-fiction to twist a narrative in creative ways. While the underlying themes of Coherence are familiar (paranoia, lost love, etc.) the way Byrkit tells his story is new and interesting. The way he twists his narrative is unexpected. He uses science fiction to tell a very interesting, very engrossing, very original story that could not have been told to the same effect with that "soft" sci-fi element.
Now, none of this is to say that there is anything wrong with more generic science fiction. I, like everyone else, enjoy films like The Martian, Terminator, and 12 Monkeys (just to name a few). But I do prefer making "soft" science fiction films (Mirror is a good example of that) and I do prefer watching those films as well.
I always go back to Fritz Lang's masterpiece, Metropolis, when discussing this dichotomy. While there is a lot of science fiction going on in that silent masterpiece, it's a story about workers rising and fighting back. It's a human story at its core, in other words. That makes it more accessible and more engrossing.
Big blockbuster science fiction films are also human stories but in a different way. Films like Star Wars or Armageddon are so wrapped up in the science-fiction element their human drama often gets replaced with melodrama. Often times those kinds of films are only trying to entertain their audience, not make them think. Again, there's nothing wrong with that. I just prefer the films that push me; "soft" science fiction tends to do that the best.