The issue is not the hamburger button per se. That is missing the point. The issue is UI inconsistency. Granted, not everyone is equally bothered by breakdowns in the consistent use of design language, but many are. You need look no further than metro on the desktop, where many claimed the jarring differences between the two made their UX with W8 unbearable. On W8 however, anybody with a working understanding of file associations could fix most of that issue, so they'd never see a metro app on their PC again, but we can't do that on WP.
Worse, I don't think there is a form vs. functionality argument to be made here. There is literally nothing in the panel opened by that button, that is not redundant (navigating files, recent and shared views works fine without it) or just out of place in a metro app (clearly belongs in the app bar or ellipses menu). IOW, there is no feature/functionality this inconsistent approach enables that a metro based design could not achieve equally well or IMHO better. Finally, the blue area up top wastes even more space than a reasonably sized pivot header would (although I agree that on many displays those headers are just too big). In summary, this approach offers nothing that a metro app couldn't, but sacrifices design language consistency regardless. That is not a good trade to make.
So, why then? I suspect MS is building OneDrive as a cross platform app using Ximarin or something like it. That would allow them to develop one app for each of the three platforms for the price of one, and allow them to release it to all platforms on the same day...
If I'm speculating correctly, I would reluctantly/rationally understand MS' approach, but emotionally hate it.