The New York Times is the last major American newspaper to be owned by a family dynasty, in this case the Ochs-Sulzbergers, a tight-knit and occasionally fractious clan who even at their best have been criticized as relics of an earlier era — generous and genteel and maybe a tad out of touch. That’s partly why former New York City mayor Mike Bloomberg has for most of a decade wanted to own the paper of record. The self-made billionaire, who’s never been impressed by the family’s management, feels he would do better, according to those who know him. And as...