XBOX One without the Kinect would be the XBOX 720, and it would instantly kill of the advantage of having Kinect 2 in every box, essentially making it a AddOn product, even for those that bought the "real" edition.
Kinect SKUs would still do everything they do now, and none Kinect owners would be encouraged to upgrade.
There are a lot of people in the world for whom Kinect will only ever have little or no value: either they are in 50 hz land, or their tv doesn't properly support the IR blaster, or MS services (and those of partner companies) aren't available, or Kinect doesn't recognise their language or just their particular voice.
Or they just want a games console. Kinect is expensive and has NO COMPELLING SOFTWARE.
For a lot of potential customers, Kinect 2 - by far (by
far) the most awesome piece of kit this gen has been turned into a dead weight by execs who don't care about games and want to try yet again to take over the living room.
Pure Gaming OS would again split the market in 2, those that can run the games and those that can't leading the developers to develop for the lowest spec'd maching, XB1 like they already do.
Pure gaming OS would run on every machine. It wouldn't need to split the user base, but dash functionality would be cut back and rolled into the OS like with the 360. When you start a game that demands the pure gaming OS the system would reboot into the OS&game, 360 style.
Full hardware access, all cores for games (time slice on 1 core per 4 core block for OS), 7 GB+ of memory, access to all those powerful DSPs in the audio block. For every Bown, old and new.
Even if they decide to reduce the price for the XB1 to the price os the PS4 it will still imho be the PS4 that is worth getting if you are only there for the games*. The same price does not make it faster. To say it a little brutal, the XB1 would imho have to be cheaper than the PS4 to make it up for the lesser power**
*favorite exclusive games can be a factor of course
**Still to be determined..
The Xbone really isn't that much weaker - and in some areas it has definite advantages. It's the admittedly clever arrangement of virtual OSes that are dragging the 360 down. It's not just the two reserved CPU cores.