This goes against the UX consistency. Now you've introduced an app that may have the same colors and icon design, but it works differently than your tablet or desktop. I really think the pivot menu is over rated. As someone mentioned, it works great to swipe through menu's in an app like Instagram , and at the same time these 4 screen's have" tapable" icons that go directly to them. However, pivoting in apps like Mint, Rhapsody or MSN Money drive me crazy --- some times the pivot swipe becomes endless, you don't realize that you've passed the section you want, some of the pivot screens have ADDITIONAL sub-menu's within them & sometimes it's just way too much with the "metro" text headers & blank space (the Rhapsody app in specific has this issue) --- it can be come inefficient easily. It'd be so much easier to launch the hamburger icon and see a full list of menu with more complex apps.
Speaking about consistency across devices, I don't think that is a good idea. Every device has it's own usage scenario. On phones and tablet you are using touch screen, while on a desktop you are using mouse and keyboard. Touch screen and mouse and keyboard work differently, so one UI across all devices can't be done without sacrificing UI either on phones or on desktops. Windows 8 sacrificed desktop UI and Windows 10 is sacrificing touch phone UI.
Microsoft should be worried about giving same features across devices and not the UI. For ex, the Photos app, collecting all the photos from all the devices through OneDrive, this 'feature' is great. Having same UI on both, not so great. Solution would be, some code added to universal apps, that makes the menus pivot if detected a phone or tablet, and makes the menus inside a hamburger if detected a desktop (which is what some people suggested here, thanks for this great idea).
Or maybe, if hamburger is really necessary to keep the one experience, move it to the right side. And enable swipe gesture for it. It will work just like charms on phones and tablets, and on a desktop, the app will have the hamburger indicating there is a menu (erasing all the confusion which the charms bar led to in Windows 8 because of lack of indication). Keep the animation just like charms, bouncy, and we are good to go with hamburgers. This will make it Metro enough and will be familiar to desktop and Android or iOS users, if they picked up a Windows Phone and will lure them into owning one.