Imagine if she tried to insure herself?
Uh, why would she do that?
Despite being super-powered, I'm sure she will receive many beatings and injuries from enemies anyway. It's part of the Supergirl character. Even the Cassandra Cain version of Batgirl, who was still a human, defeated and injured her. In the 84 film, Supergirl was battered about quite a bit.
Oh, and she did injure herself when she tried (and failed) to fly and crush a rock a rock in The Phantom Zone. Falling into a tar pit didn't help, fortunately her old mentor picked her up out of the pit and carried her to safety.