So, let me pitch you some vaporware. Let me describe a game concept. We'll call it "Unbioshock".
For once and only for this essay, I'm not ragging on Bioshock. I am talking about a completely different game idea that I thought was interesting. One inspired by Bioshock. It's still set in the same place, still thematically centered around escaping from cages.
In this game you play a woman who has been locked up in a tiny apartment with a big library. The game starts off there, allowing you to get used to the controls and get a feel for the life of the character. It also lets you get familiar with her hands: she's right handed, but her right index finger is partially missing, replaced by a classy thimble. It's her index finger in our version because we need to have a good reason why she's fit enough to leap fifty feet and zoom along a rail one-handed, but can't fire a gun.
After you summon and send away your bird guardian with the whistling pipe song, the player learns to lockpick and tries to escape. The same pipe song plays and summons the guardian, who takes you back to your cell. You try to run or hide, but it has no problem catching you.
Shortly after this, a man comes and breaks you out of your apartment. This is where the game proper begins.
The game is all about finding a way off the city. Nobody wants to kill you, but they all want to capture you, and you're a frail person who's never been outside her apartment. So you rely heavily on this guy who rescued you. He does all the combat stuff. But there's two problems.
One is that he's dumb as a brick. This means not only is he constantly taking on more than he can chew in combat, it also means he can't actually figure out how to get off the city. You have to help him in combat by tossing him supplies that you find while scrounging around, and patch him up after combat in a doctor minigame. You also have to find the way through the city, picking locks, finding maps, working machinery.
The other problem is that he's a villain. He's violent and wants to take you someplace just as bad as you came from. So there's a big part of the game which is about handling this guy. If you lead him into fights, he gets upset with you and short-tempered, but on the other hand he'll realize he's out of his league in this city. If things go smoothly, he'll be polite and happy... but he'll also be very controlling and dismissive. His opinion can also be affected via other means, such as how you behave towards him, what weapons you insist he use, how you dress, and how you interact with other people. How much money you toss him vs how much money you keep for yourself to spend wisely.
But you notice, there is not really a "good" side to this axis. The brute is either bitter but begrudgingly respectful, or pleasant but extremely controlling. The last choice in the game is whether you free yourself from the thug to live a dangerous life on your own, or whether you trust the thug's judgment and stay with him in a now-hopefully-well-meaning cage.
So the theme here is one of safety and control. It's very much a matter of escaping a cage, just like Bioshock Infinite, but here instead of being a walking death machine, you're someone who is actually in serious trouble. Escaping the cage isn't simply a matter of walking out and then life is hunky-dory: escaping the cage puts you in an incredibly dangerous situation.
You don't even need the magic powers to make this game float. It floats well enough on its "thug management" mechanics. You just have to make sure that the thug can't actually die: he always wins his fights, but the more torn up he is at the end, the less polite he's gonna be. (If the thug can die, the game becomes a particularly nasty escort mission.)
The gameplay itself is half about immersing yourself in the world. There's no fighting mechanics for you: while you're wandering the world, nobody will shoot at you and you can't shoot at anybody. You may occasionally have to hide or run, but by and large you just wander as you please (as long as your thug doesn't object). In the world is a scrounging/supply mechanic, where you look for things and toss your thug things.
The other half of the gameplay are the minigames. Mechanical puzzles, lock picking, and patching up the wounded. These are what allow you to manipulate the world, sometimes to move forward, but sometimes for other advantages. For example, dropping a crate so your thug has cover, or healing an injured soldier that later helps you bypass a fight. Sealing doors, lighting or blacking out hallways, making noise, overloading an energy conduit to make it explode...
The minigames are not always as tension-filled as a first-person shooter would be, but they can be quite tense. As you can see, during combat your primary role is to manipulate the world so that the thug doesn't get too shot up. Sometimes this means doing something to the combat situation (catching some of their attention and leading them on a chase, or sealing a door, or whatever). Sometimes this simply means picking a lock while your thug holds off the hordes.
Anyway, it's an interesting thought. I'd love to play a game like that.