Things like Dyson spheres need a whole lot of raw material, which is rather difficult to come by, since the elements needed for good structural steel are scattered fairly thinly into the universe upon the death of the stars that produce them.
The obvious solution is to somehow get at the approximately one solar mass of iron while it's still cooking, or at least before it has time to fully disperse, which would be before the star turns into a neutron star which is even harder to mine. Supposing you have the world-smelters and transport capacity to strip mine several solar systems' worth of planets, how would you go about shutting a star down so you can get at the layers of heavier elements of the inner layers of the star?