i'd agree that it makes no sense except for the part where we're having a conversation about stone Angels that displace people in time. and i'm not trying to be snarky, but serious. it's *so* made up that, if done correctly, holds its own internal rules: see Tardis.

while your point about the Dalek ep holds well, i'd argue that the Angel "ability" flies better for a couple of reasons. the first, the simplest, being the scene was played soooooooo much better than the Dalek denoument, and had more substance and tension to it, so it felt, meatier (?)

but second, and more importantly i think, there is already existing mythology in most cultures about the power of the eyes to the soul. i think, imho of course, that Moffat wove that skillfully here. that Dalek nonsense was pulled out of thin air, but the Angel "ability" had some depth to it in mythological terms.

if you then add that to the Angels' existing ability to manipulate space/time, however haphazardly, and they clearly have some mojo goin' on. ymmvoc