Why an Invincible Heroine isn't a bad idea

I may have mentioned already that, due to reasons I'll have to explain with a plot summary, she has accidentally become invincible.
Now, this may seem like a bad idea for a game, But I've been playing games for a while now, and death seems to often become just an inconvenience anyway. You just lose a bit of time and reappear back at the start of an area. I figure that since Lena's going to be running around on top of cliffs, falling and being stuck at the bottom of the cliff again is enough of an inconvenience as it is. If she is invincible for plot reasons, it means she can fall a long way without it being a problem, like characters in early platformers from when I was a kid, only they didn't have any kind of explanation for why Sonic and Mario were capable of falling fifty feet and coming away injury free.
It also allows for Lena working with realistic physics, but still being able to do things and go places no sensible climber would without all the faffing about with harnesses.

Invincible protagonists aren't technically a new thing, it's just that normally it's not explained. This way, we also get the explanation for why on earth a reluctant young lady is out saving everybody by doing insanely dangerous things. It's because she's invincible and therefore sort of obligated to do so!

Without the pressure of harsh time limitations or limited lives, the player has more freedom to explore, mull things over and try things out. The game won't penalise players for trying out a novel way of getting around an obstacle or exploring a hidden area.