Hiromu Nonaka, second from left in the front row of a photo of Japan’s 1998 cabinet that hangs in his office, and at right last month. Mr. Nonaka rose to chief cabinet secretary, but as a descendant of a class of outcasts further advancement was blocked.Credit...Ko Sasaki for The New York Times KYOTO, Japan — For Japan, the crowning of Hiromu Nonaka as its top leader would have been as significant