The Dyson Sphere would need to be at a significant distance from the black hole for several reasons including:
It is really really hot close in. And there is a lot of matter flying about at significant % of c. So there's all that pesky collision damage and melting
You need to have enough matter _inside_ the sphere to keep the power going for a very long time.
It will take _a lot_ of material to construct a sphere of that size. And the sphere itself would block infall of matter from outside.
So at the very least, it would be a giant PITA to construct.
In theory, we could capture the output of thermonuclear weapons, too. But some of the same problems prevent us from doing so with current tech.