I know a little about acoustics and mixing, and I have a working theory on the perceived loudness of TBA vs other venues on TV broadcasts. That being said, I am certainly NOT familiar with the amount of microphones used in production or their locations, so this is just my speculation based on aural analysis. Unfortunately, anyone familiar with music/sound production can tell you that the finished recorded/broadcasted product can sound drastically different than the live performance, so idk if we can know for sure without someone from the actual production team chiming in. My best guess is that TBA sounds quieter than expected on TV due to the distance that the sound waves have to travel to get to the microphones. I think smaller venues with less air space effectively concentrate the sound waves and sound bigger on TV, even though the sounds are not truly as loud as TBA. In short, perhaps the fewer people in the crowd of smaller venues are just closer in proximity to the microphones than at TBA. That may not be entirely accurate, but I'm pretty sure the shear size of TBA is playing a significant hand in this.
I know how loud TBA can be (utterly deafening), and it seemed like that was the case yesterday, even over TV imo.