In this case the energy that goes into creating the e+e- pairs far outweighs the energy you get out. For example, given that this is Quantum Mechanics, there is a non-zero but not necessarily close to one probability of creating a pair from a given pair of photons. One could imagine the other light that didn't interact would just escape to the environment. You can conceptualize this as an photon produced to pair created efficiency, and I don't see it for any reason being very big.
Then again, I'm not sure I understand the experiment, for example, I'm not sure how a blackbody spectrum helps in the breit-wheeler process. I think that the light colliding at a perpendicular incidence helps, but other than that, I can't see how the spectrum of radiation matters...like how is using a blackbody spectrum is better than, say, a monochromatic laser? I think I'd have to look at the paper once it gets out.