I would rather know my child is dead than to think about and worry about her being raped, beaten, burned, forced to live underground or in a hole for years. My DH feels the same way and so do a lot of people I know. Her being home safe and sound after potentially years of going through this, isn't worth it to me. AGain, many things are much worse than death.
I wouldn't want to go through those years wondering what was happening to my DD while I was in my nice comfy home, and she was having God knows what done to her.
Elizabeth was missing for 9 months. It wasn't years. Maybe if she'd been missing for quite a few years I may agree with your sentiment but in your example she was gone for 9 months not 9 years. I went and searched for her when she went missing. Listening to her parents/family talk about getting her home was very sad but the amount of love and hope they had was inspiring to me.