Ah...well, that answers that. I think the piece I was missing is that the presence of a black hole in any system doesn't necessarily destabilize that system. Thank you all for helping me understand this better. I think I get it now.
I was thinking about the supermassive black hole that is theorized to be at the center of our galaxy, and indeed, at the center of most galaxies. If that black hole is continuously consuming the stars, planets and gas around it, given enough time, will it not consume the entire galaxy that...