In one of my Physiology classes (my BA is in animal behavior which includes pain _expression_) they had cuttings of cow hide for us to look at under microscope, as well as in drawings. The nerve endings went through the skin just like ours. Yes, the skin is thicker, but the nerve endings still reach the outside layers as to warn them of pending danger. When the cattle rush through the barbed wire, they do not yell ouch like we do, true, they project pain differently, but that does not mean they are not experiencing the pain. We expect animals to show pain the same as we would show it, but not all animals show pain in the same way. Many animals will hide pain and illness so they are not the one that gets attacked by the lion(or human) who will go after the weak.
Since people see cows not showing pain as other animals might, they think there is no pain. But there is, they just hide it as to not appear weak to the animals preying on the herd. It is instinctual to hide it from the lions (or humans) about to attack because lions prefer to attack the weak, ill, or otherwise easiest catch.
Someone also asked what alternatives do I have, barking that I am just complaining with no answers...and you are right, I don't have all the answers. Dogs and cats are being injected with a little identifier. I am hoping this will continue to evolve. Someone else also told me they are doing electronic buttons now. Maybe this will get easier as our technology improves and gets less expensive.
In the mean time Freeze branding may be better...I really don't know about freeze branding either.