No disrespect, but Kristoff isn’t letting her choose here. Sister or no, Kristoff would never ever ever ever ever let Anna throw herself in front of a sword. He’d throw himself in front of a sword if that would stop her. The problem is that he’s too far away, too far to stop Hans, too far to stop Anna from stopping Hans, too far away to do anything other than let the scene unfurl.
That expression isn’t Kristoff painfully deciding to let Anna choose Elsa, that’s the expression of panic as he realises what she’s about to do. That’s the expression when he realises that all hope is lost. That Anna is going to freeze, or even worse- be sliced open by her fiancee.
In any other context Kristoff would let Anna choose Elsa without a second thought, but he would never let her kill herself for either of them.