Don't black holes suck-in all kinds of stuff all the time, making it a bad place to be for an energy plant?
Black holes don't suck anything in. They just have very strong gravity relative to their size. So just like a space probe would drop into the sun if it got too close, things can get into an inescapable orbit around a black hole. If you can build a Dyson sphere around a star you can build one around a black hole of a similar mass.