Similar foods exist in parts of China and SE Asia, but it only really took off in Japan.
“By the eighteenth and early nineteenth centuries Tokyo, then called Edo, had usurped Kyoto as the capital of Japan, becoming the largest, most populous city on earth in the process. A series of fires, however, threatened the future of the world’s first conurbation, and so open flames were banned in restaurants and the city’s burgeoning fast food industry was virtually wiped out overnight. To the rescue came sushi, which could be assembled without the need of a flame” Sushi and Beyond page 172
Sounds too convenient an explanation to really be true. Any other ideas?