Not in all cases. Which is why apps have an API where they can turn it off if they want to reclaim that space for their own use.
Interestingly, no on ever figured out how to implement this trick when apps wanted to use their hardware buttons for extra screen space. I suspect this is a big reason for this particular compromise.
Maybe, but look at the bezel at the bottom of the Pixel, plenty of room for software buttons, we just don't have full edge to edge screens yet in all directions. So with plenty of room we are choosing to waste screen.