From a neuroscience perspective it would seem obvious that neural networks can work with less than 8 bits. According to a study from 2015 [1], the synapses in the Hippocampus can store about 4.7 bits of information (26 discrete connection strengths). While the real brain graph is very different from a transformer, I think this should still be achievable for other architectures as it is most likely just a question of extra stabilization during training.