Anonymous marking was, iirc, introduced to reduce bias in marking - or rather, to filter out some of the cruder kinds of prejudice. I'm not sure how anyone who's ever taught, and marked, can uphold this myth, despite the convenience of doing so.
For a start, the scripts can at best be pseudonymous, as they do not entirely lack identifiers. However, even that is disputable - in a system where student numbers are constructed out of a recognisable combination of surname consonants and first name letters, it's easy enough to guess who the students are from the student numbers. And given that one has typically been working with the students for a whole semester, one knows them by their student numbers almost as intimately as by their names or faces (in the case of absentee students, perhaps better!)
And then, of course, their handwriting leaps off the page at you. Despite wordprocessed assignments, plagiarism declarations still contain samples of handwriting and it's very difficult to ignore all the signs pointing to the person behind the script you're marking.
Perhaps in some cases this is a problem; however, most marking involves a fairly robotic process of entering the zone and spotting what you're looking for, and afterward trying to conform to some kind of normal distribution more or less so that not everyone falls within a percentage point or two of 65%.
But then again, myths persist because they serve a purpose, so perhaps we should quietly smile and nod, and continue with our marking without thinking too hard about it.