Microsoft has a lot of manufactured Kinects sitting in warehouses, that's going to end up as a lot of unsold supply if they offer a Kinect-less SKU. Separating the two isn't as simple as you might think.
I've considered this as well.
I think we all have to remember that while the Xbox One hasn't sold as well as MS wanted it to (what with the massive supplies the system had earlier this year and at launch); they are still at a statistical tie with PS4. Slightly less, but not that far behind. The problem is that they are getting whipped everywhere else while tying in the U.S. Worldwide, I don't Xbox One stands a chance, but U.S. is still very possible.
Realistically, Microsoft wouldn't have to get rid of kinect and drop $100 dollars off to beat PS4 in America. All they need is a $50 dollar price cut. The thing is, I don't think Microsoft wants to sell the Xbox One at a loss for an extended period of time. Though they certainly could, it would be dumb of them considering they could just take the kinect out.
Why would they want to take kinect out? (As far as I know) Kinect games aren't doing very well, or at the very least not as well as MS anticipated.
If MS doesn't win March npd's after price cuts at multiple major retailers and arguably their biggest game of 2014 for free... Kinect will be gone by August.