Now you're into a matter of matching product to customer.
Most taekwondo schools, regardless of org, are family oriented schools. As an org, the ATA has focused on this market.
Honestly though, how many perspective customers actually go to the ATA, WTF, ITF (aren't there like three different ones now?), Kukkiwon, or ITA websites? They go to "the local karate school" and whatever they've got, that's what the customers get. And if there's more than one school in the local area, they'll go visit them and see who's after school and summer camp program is the best. If all things are equal, they go where their kids friends are or to the place that looks the most professional. They don't know enough to ask the kinds of questions that you or I would.
As for people thinking that what the ATA offers is taekwondo, well... it is. Just as ITF and KKW are. Besides, the only people who will "look at these videos and think that THIS is TKD" are not informed enough to know what they're even looking at. You and I see technique and style specific things in these videos. The novice or beginner sees people in gis with belts jumping around doing karate. That is it. They know only that they can't do what is pictured.
Look, the ATA has a very comprehensive program, meaning that every aspect is codified, unlike the Kukkiwon that has a very basic program and says, 'round it out with whatever you feel like.' The ATA has built in BBC, leadership clubs, little ninja/dragon/tiger/munchkin programs, martial weapons, and optional XMA. Join the org, get the curriculum. If you sign up, get your BB and find that you want something a little more traditional or different, go on and branch out.
But their curriculum is their curriculum and you may not like it, but they aint dummies. Their curriculum is one that attracts people and keeps them happy through BB and brings the org good income. Organizations are in business to stay in business. Their formula works well for them. Not my cup of tea, but it is the cup of tea of thousands of kids all over the US.
It is their brand of taekwondo. It is their niche. ITF fills a different niche and the KKW fills a different niche. The independents and other smaller orgs also have their respective niches. The pie is plenty big. We can all eat at the same table.
Daniel