I absolutely agree. I'm sure flat is fine for phones and small screens where windows never overlap, but it's useless for a big screen where they do. I'm constantly mistaking an open window for a sidebar box on a web page for instance, or thinking an app has opened a web page, when all it has done is opened on top of one.
This is a really really silly design decision - seems to have been motivated just to make the interface look more hip and phone-y or tablet-y. Completely inappropriate for a windows environment.
A fix to get some kind of shadow or other solution back would be greatly valued, and MS take note.