Child-free flights

Help me settle a gentle argument. Four of us were on a flight with A LOT of children. None of us dislike kids, but it felt like it was for vacations, not for moving or whatever.

Three of us said some legs that were without children would sell like hotcakes, but I kinda disagreed. I think it would have to be an airline specifically for it, with limited segments compared to Delta that had AUS to BOS direct as child-free (example).

So I'm trying to do the math, but I really don't think a major airline could have exclusive flights.

I know there are child-free cruises and restaurants, so I don't think it would be illegal in America, but I can't imagine some of the longer flights being full as people sometimes need to bring their kids (moving, seeing grandma, etc.).

Thoughts on viability? (NOTE: this is a somewhat light-hearted discussion, not opening up rants about kids on flights, or whatever)