I think that way of thinking is something that came up in recent years. Maybe I'm wrong, but I thought teachers used red ink because it made the marks stand out so the kids could see exactly where they made their mistakes. That's especially true if they're grading reports or English papers and marking all of the incorrect spelling, punctuation, etc.
I don't see a problem with it, but some people will say the red marks are too visible to other students who may looking around and the student with the bad marks will get embarrassed. I think as silly a reason as not keeping score in sports for the little kids so they don't get upset when they lose.