I mean. This is like saying anyone should go and fight in a war where they may or may not contribute to winning it and survive. It's even quite pointed out by her teacher that the way she was going about things she was going to get herself killed.

She spent a thousand years training for it. She really has no idea how much time she needed to train for it or how much power she actually required. She's also lost to others in that time, there are people that can beat her in a fight. She's not some special chosen one, just a person with a grudge who trained a very long time with the skills specifically necessary for this one task without really knowing how much was needed. I don't think Frieren is afraid of death, or even injury, she seems very much to enjoy battle in a way that seems a little bloodthirsty to be honest, but I don't think she really ever knew whether she was enough to win or not.