It's not as exciting as you think it is. "emissivity higher than 0.99 over a wide range of wavelengths" is basically code for "it's, like, super black"

The limiting factor isn't the emissivity, it's that you're having to rely on radiation as your only cooling mechanism. It's super slow and inefficient and it limits how much heat you can dissipate.

Like the other person said, you can't do any better than blackbody radiation (emissivity=1).