To expand a little on something, when I say "I don't think they [the Legion] get seen as superheroes the way the JLA do," I don't mean they don't get seen as superheroes. It's in the name, even.
But I think there's a different quality to what "superhero" signifies in the Legion's era.
If the...
...JLA was like the JLA we have now, but everyone in Illinois had superspeed and Barry was the best at it, and everyone in California had a power ring (of wildly-varied strength) and everyone in Connecticut could shrink, and so on, we'd think of "superhero" differently, too.
The Flash wouldn't...
Do they work today as a concept? They always seemed to me like a weird blend of silver age goofiness and a continuity that is intimidating even by comic standards. Is it possible the best place for them at the moment is as a little side setting for other DC adventures?