I don’t think it’s that simple. My assistant professor friends build relationships with students and help them work on topics and weaknesses. They get to know students and how to help them on problem areas.

For deeper courses they may help them pick topics to write about and sources to read.

Having that context for the ongoing feedback from grading and mentoring is valuable. Depending on the work it simply might not be possible to do anything blind.

Even without names, handwriting and writing styles are obvious. Even in an office setting I can always tell who wrote something as small as a sign or a note by handwriting or word choice alone.

Yes, unless you have the grading done by someone else in some sort of double-blind setup, or replace everything with computer-graded multiple-choice questions, you're still going to be pretty identifiable.

You would have to separate the teaching and assessment functions entirely.