I think the problem with your thinking, and something that I've been trying to figure out as I sit on/direct more interviews myself, is that this doesn't actually tell you that the candidate can't code, but just that they couldn't code in that setting with that problem in the way you chose to frame it for the interview.
Meaning, I often sit with candidates who come in with 3-5 years experience in industry who can't do a relatively simple programming task. That can either mean that we consistently are drawing applicants who have been pulling the wool over the eyes of their past employers for 1/2 a decade, but actually can't program.
Or, it could mean that they get incredibly nervous coding in front of strangers, aren't used to doing more abstract problems, and once they realized this, experiencing a "snow ball effect" of nerves, wherein they train wreck in the interview.
Meaning, I often sit with candidates who come in with 3-5 years experience in industry who can't do a relatively simple programming task. That can either mean that we consistently are drawing applicants who have been pulling the wool over the eyes of their past employers for 1/2 a decade, but actually can't program. Or, it could mean that they get incredibly nervous coding in front of strangers, aren't used to doing more abstract problems, and once they realized this, experiencing a "snow ball effect" of nerves, wherein they train wreck in the interview.