I wonder if anybody at Harpers ever looks at the numbers to decide if the popups should stay? They should have a minimum success rate that, if signups drop below, they get rid of the popups.
I'm not sure what you mean. For every thousand times it's displayed, how many times does the person viewing the page just close it and not act on the offer? If it's less than some very low number (maybe 30%), don't show it.
Or maybe show it after the article has been scrolled all the way to the bottom. It's a long article and at that point you know the reader might be interested in seeing more from you.
You're assuming Harpers is optimizing for not nagging people. That is not the case at all. They are optimizing for collecting email addresses. If you do not want to enter an email address and bounce they lost nothing, you weren't going to provide an email anyway.