I was thinking the field of astronomy would need to survey the satellites, in order to make sure it doesn't interere with any of their observations of the stars.

So, they would erase the stars, but only to create a satellite mask, generally speaking.

Actually, this is pretty common for non-scientific astrophotography! Erase Stars -> Edit background and stars colour, contrast etc separately -> Recombine!

Why not? Stars are boring, the cool things are galaxies.