The moment they are seen by any other living creature they freeze into rock. No choice, it’s a fact of their biology. In the sight of any living thing, they literally turn into stone. And you can’t kill a stone. Of course, a stone can’t kill you either, but then you turn your head away. Then you blink.
That’s why they cover their eyes. They’re not weeping, they can’t risk looking at each other. Their greatest asset is their greatest curse. They can never be seen. Loneliest creatures in the Universe. And I’m sorry. I am very, very sorry. It’s up to you now.
I’m always a fan of the weeping angels being fallen timelords after the war…