Is the refresh really a big power draw vs the backlight or even the pixels themselves? I think the thing about e-ink is that it's a chemical producing/retaining the pigment, rather than a light source. So even when it's off, it retains its current colors. When a LED is off, it's just... nothing.
But you still have a point. Even if a LED display has "only" a 2 or 3 day battery life, that's still pretty huge to mere hours.
How do smart watches (like the Garmins with 1-week batteries) do it?