having content areas fly in for almost a whole second is overkill
...except for those cases when it's not. Major context changes such as switching applications benefit from more explicit animations, that physically convey where everything goes or comes from; those can run from less than half a second to about two seconds for more showy "Welcome to product X" screens. If the old interface simply disappears, the user has no clue on how to restore it. That's why you get nifty "minimize" animations in all modern desktop environments that care about more than processor cycles.
In the Material design, animations are also intended to increase affordance by showing what areas are interactive, without requiring the extra chrome of everything having 3D borders.
I think you misunderstand. I'm not against animations. The minimize animation in today's operating system is a perfect example of how animation can simplify the user experience (although I do think the OSX shrinking animation is a tad dramatic). But keep in mind, those animations are still short compared to the examples here. Whats more, the linked example uses the fly in animations for interactions without major context changes. Switching from pages in a document is hardly the same as switching applications.
In the Material design, animations are also intended to increase affordance by showing what areas are interactive, without requiring the extra chrome of everything having 3D borders.