Apart from the vantablack heating issues sibling comments have already mentioned, you'd also need to take into account the energy used by the cooling system for the cold end of the TPV. In practice you'd need to pump either water or air past some form of heatsink and the energy consumption of the pumps would reduce the efficiency below that of the 40% of just the TPV.
This would be a heck of a lot of waste heat to deal with. You could probably boil water with the leftover energy to turn a steam turbine to power the cooling apparatus. A dual stage solar plant.
The reason for the high level of waste heat is that the system has to operate at thousands of degrees C. There is still a huge potential above room temperature. Most systems work closer to room temperature so there is space to squeeze them in after this system has extracted all of the energy it can.
Yes, but the pumping power is about 0.2% of the total power, so this is not a significant consideration in practice. If it was, people would use solar chimneys instead of mechanical fans and pumps.
