> but then lets the waste heat just pour out

There is no other alternative! If I build a perfect Dyson sphere and capture the energy output of a star, all of that energy will become heat. The average surface temperature of my Dyson sphere will be (IIRC) the ratio of the surface area of the sphere to that of the contained star, multiplied by the star's effective surface temperature.

"Recovering heat and making use of it" requires a heat differential. You need a cold side and a hot side to use energy. Using that energy causes the cold side to heat and the hot side to cool, until they reach equilibrium. The further the difference, the more usable work you can do. The closer the two sides are, the less work you can do.

Someone else here said it best: waste heat is the graveyard of energy. Once you have used energy, it will become high-entropy, low-grade, diffuse heat which is difficult-to-impossible to extract further work from.