If it's a peripheral of every xbox one like its guaranteed to be, then of course they'll use it. It's another input method, there's some exciting things that could be done there.

Yes. A lot of the games coming out for X1 are using it. Two examples are Battlefield 4 and Dead Rising 3. In fact, you have to have the Kinect on in order to play Dead Rising 3.

Most games are made for xbox ported to ps4, thus Kinect is there, and removed for porting.

Did developers use the Wii U Gamepad? [spoiler]In all seriousness, I love Nintendo and I hope they turn the Wii U around[/spoiler]

If Microsoft makes Kinect a vital part of using the Xbox One, players will be asking for developers to use it in their games. The use of Kinect for UI navigation and performing actions, coupled with the exclusive titles that take advantage of it, will demonstrate to gamers how Kinect can boost their gaming experience, and demonstrate to developers that it can be done. Eventually, players will associate Kinect actions with the Xbox One itself, so that games for the Xbox One will be "missing something" if they lack Kinect support. Not utilizing Kinect will be akin to not putting a touchscreen on a smartphone, and users will feel as let down as when they tap on the screen and nothing happens. Certain gestures and voice commands could become standardized, like controller layouts are now; even if you've never played this particular FPS before, you still know which sticks move and look, and you expect actions like aim and reload to exist. Obviously, that's the "dream scenario" for Kinect 2.0. It's possible that Kinect will flop and Microsoft will un-bundle it from the Xbox One. MS will spin it as a "budget option" or whatever. But Kinect has two good things going for it: it's the easiest way to use some of the Xbox One's features, and it recognizes far subtler movements than its predecessor, allowing developers to incorporate more natural movements than arm-flailing and jumping up and down.

Plus none of the other platforms have a camera that can be utilised in the same way?

Nothing major needs to be changed, but if you can fully utilize something to make your game better, why wouldn't you? The best example I can think of is how Skyrim is with Kinect. Switching between items, shouts, magic, or telling a follower to wait/follow is pain that slows down gameplay and increases your time in menus. If some voice commands can alleviate that, why not allow for it? And hell, since more games are starting to use emotes now, I'd rather do a wacky arm flail to wave or salute, rather than having that take up valuable button space.