Such is the life of a magazine-cover junkie. Or, rather, the Cover Junkie, who obsessively curates the best of the editorial world for around 120,000 followers on Instagram.

National Lampoon ’s 1973 cover “If You Don’t Buy This Magazine, We’ll Kill This Dog” became a classic, and was ranked at No. 7 in the American Society of Magazine Editors’ “Top 40 ...