I think you're right: it's impossible to eliminate biases completely, or adequately. And therefore we need to come up with alternative mechanisms to do it for us. One is the method of science that you mentioned. Another is increasing group representation. For instance, most feminists are female. This means that, even with the best of intentions, they will tend to be very aware of unfairness directed toward women, and relatively blind toward unfairness directed toward men. Only when 50% of feminists are men will there be hope for true justice. These are just two examples of many ways we can outsource objectivity, even when it goes against our nature.