“Lately I’ve wondered if there is a fate worse than closure: watching an establishment pander itself to the nostalgia-loving influencer crowd in the hope of going viral. Are these the only options available to our legacy institutions?” writes Charlotte Druckman. She had noticed that some of the landmarks from her own childhood had, in recent months, become more active on social media and in press outreach. “When the limited-edition Barney Greengrass dad caps dropped, I knew there was no going back,” she writes. A generational turnover is playing out at Barney Greengrass. After a 2019 Instagram announcement that the restaurant had “joined the digital age,” the restaurant barely posted until earlier this year. Just like that, third-generation owner Gary was all over the feed, grinning beside Arnold Schwarzenegger or Martha Stewart, or posing with Andy Cohen. The store’s recent limited-edition Knicks shirts, along with two-toned dad caps and some limited-edition World Cup–themed jerseys,...