Mildot, you are missing her point. You do not have to have a brand on your animal for brand inspections to be legit. They record markings and scars too. For some people, that is the only actual proof they have that they own their horse. So if your unregistered horse is stolen and the police recover it, you can actually prove that the animal is yours instead of depending on them taking you at your word.
The reason that some places still require it is antiquated, but still legitimate. Rustling was much more common in the western states than it was the eastern states. With brand inspections being required, then thieves had a harder time selling the stock that they stole.