Well, you could argue that list of skills, education and work experience could bias the assessment as well. There's no clear-cut line here that separates relevant from irrelevant.

Sometimes even gender is relevant. For example clerks in grocery stores are mostly women and there are bunch of good business reasons for that (even if they are based on stupid social biases, those biases still are real and business value can be extracted from them).

Also, once a shop commits to a particular gender choice, it might be inclined to stick to it exclusively. For instance, I heard a first-hand story from a local grocery store about why exactly it avoids hiring men (especially attractive ones) for clerks - because it leads to relationships forming between co-workers, which usually end with people left jealous and/or angry at each other. I can't really blame that shop for this choice, it is a rational one.

I'm not responsible for hiring decisions right now, but if I were then one thing I wouldn't want to be anonymized are names. I do believe in the concept of maintaining blacklists against well known cheaters, spammers and other evil doers, and anonymizing names makes you unable to discriminate people by level-of-assholiness ;).