You can help this along by ignoring the way her tenure in Congress seems to have been soft-retconned out, too. As a public figure, that would have gotten a lot of coverage that she wouldn't get as just "the Commissioner's daughter" (particularly since I'd expect a world toward the ideal end of the scale like the DCU to adhere more closely to journalistic ethics about private citizens). Though it gets complicated when you remember the retroactive alienation of the Bats and the excision of Kara from the timeline; post-Crisis, the circle of people who knew Bruce Wayne was Batman narrowed to, like, Clark, full stop, and of course Babs didn't even have her Super anymore.