Thought I'd add my $0.02. I finally got around to opening my Smart Cover. It seems a little thicker than my Air 2 one which I don't mind, but the over flap isn't nearly as bad in real life as it looks in pictures. Here are two pictures and one has a #2 pencil next to it for scale.
It is slightly annoying, but I don't find that it "digs" into my hand or presses up the cover, but maybe that's how I hold it. I've never pressed the edged of the device right against my palm even when carrying an Air 2.