I think it happened in the 80’s I think the triple whammy of DKR, Year One, and the killing Joke pretty much rocketed Batman past everyone else. Prior to that Superman was the most popular character, and Batman was seen as kind of corny by the population at large( a result of the 60’s show). I feel giving Batman consistent mythology also helps. He’s the only character at DC that doesn’t get radical transformations after every major reboot. Their is no “Zeus’ daughter now” moments with Batman like their is with pretty much every other DC character.