Is there really a need to fail a high school student if a name is missing from one answer sheet? The teacher would automatically know whom it belongs to. They all know each other and interact every day. If there are multiple answer sheets missing names, it only becomes more dodgy. This is entirely different from taking a university entrance exam and forgetting to write your name. Everybody's a stranger there and it's not the staff's job to help the applicants in that sense, whereas a high school teacher's entire job is to help their students to study as well as possible. Depending on the situation, I suppose the uni staff could check the name field immediately when the papers are handed over, but that's about it. It's a competition anyway, to see who gets in, so the staff helping a single person would be biased. High school exams aren't a competition, they are meant to make sure students have learned.
But then again, it's Japan, so I can totally see it happening.