As New York City’s new mayor prepared to take office late last year, a local tabloid decided to show him who really ran the town. In a series of outrageous covers, the New York Post humiliated one of the mayor’s longtime aides with racy photos, and headlines like “Give her the heave-ho, de Blasio!”

In the end, the Post prevailed (after a nasty “Ho! Ho! Ho!” cover and stories early this month about toe-sucking) and the embattled aide quietly left the mayor’s team. The ousting was a clear victory for the Post, yet it also felt like a swan song. It was a reminder of how the Post and other tabloids have for years browbeat local politicians to shape the agenda of a city, but are now struggling for relevance amid a cacophony of online media noise.

The decline of papers like the Post represents the end…