That's what's been done so far [0], both on the ground and in space. As I understand it, the further your disk is from your telescope, the better. But your stick needs to be rigid enough to keep the disk exactly in its place. And a rigid stick has weight.
For Proba-3 the goal is to have the two satellites more than 100m apart. If you want to do that with a stick, your stick has to be longer than the ISS. That should tell you a thing or two about the complexity and cost of building and launching that stick.
I do have to admit I'm not exactly sure what the advantages are of having the disk further away from the telescope. I suspect it's to do with the interaction between the light and the edge of the disk, but I'm not sure.
For Proba-3 the goal is to have the two satellites more than 100m apart. If you want to do that with a stick, your stick has to be longer than the ISS. That should tell you a thing or two about the complexity and cost of building and launching that stick.
I do have to admit I'm not exactly sure what the advantages are of having the disk further away from the telescope. I suspect it's to do with the interaction between the light and the edge of the disk, but I'm not sure.
[0] https://en.wikipedia.org/wiki/Coronagraph