Mad, Mad Multitasking
The bald assertion that "the less time the user spends in the app, the more productive they're going to be" sounds nice, but does not seem to have much in the way of proof behind it. In fact, it looks a lot like other pushes by Microsoft to overhaul the user interface without checking to see what actually works for its customers. There have been plenty of studies which clearly demonstrate that people who think that they are quite good at multitasking are actually deluding themselves (many have been done to demonstrate that texting while driving is a bad idea). This looks like another way to fragment the user experience, even if it is not done on a visual level. If you are bouncing around between tasks, even if it is not reflected by what's on the screen, your overall productivity will go down.
It also looks like a way to dumb down the user interface to the lowest common denominator. People who cannot type might be able to input info into a Word document a lot faster with Cortana to start with, but will not be able to ramp up to the speed that someone who really knows the application can achieve. Similarly, I suspect that this will hold true for working with computers and apps in general. This tech might make things easier, but I do not think it will make things better - and that is my unsubstantiated assertion.