They should have given Dodai (the rubber guy) Byakugan
as the title says.
Dodai has an eye patch, over his left eye.
Ao, the Kirigakure sensor, has one over his right eye(with a byakugan).
Both are sensors and work for HQ in the war.
It would give an interesting story if Kiri and Kumo worked together in the past and took down a hyuuga.
One eye went to Kiri, Ao, the other to Kumo, Dodai.
Although i dont think its likely to happen.
He would probably have used it already vs edo third raikage, if Dodai had one.