Probably a more robust test would be asking the caller to run their hand through their hair a few times. Maybe you could pre-render a few samples, but it would be trivial to request the person pass their hands through their hair in a specific way, or simply do it again after their hair is already messed up a bit from the first time. It could still be defeated by the caller having the same hair style (or wearing a good wig) as the person they are imitating, but then making someone look like someone else with practical effects has been a thing forever and it has not been a huge problem.