The media would totally throw a fit over what Supergirl did. The problem was I think the scene itself was pretty weak. They pan to the kids who are all either cringing or looking terrified, which would just never happen imo. At best you would get a mixed bag of different reactions. I think most of the kids would lean towards fanboying / fangirling over Supergirl unless she straight up murdered puppies or something, because kids just naturally want to like superheroes. The point is that Supergirl is unimaginably powerful (to everyone else), and she's still new, so you have no idea how she can react to certain situations. Superman? He's been around for about a decade, so most people who pay attention know his MO, but you can't say the same for Supergirl. Even then, I bet some people still think Superman is utterly terrible and they're just a minority at this point. Can you just imagine the media blow up, with one side flipping out over how Supergirl is gonna straight up murder everyone, while the other side went "Holy crap wait up here, can we not jump to conclusions for once???" But the show couldn't show that, so instead weakly showed a group of kids all looking terrified. I doubt a group of kids would really all be terrified. Probably should have had maybe some small, younger kids in the mix, and they could maybe look scared, while the older kids were still like FUCK YEAH, SUPERGIRL, and then some Concerned Adult could step in going OMG SUPERGIRL U A BAD ROLE MODEL, YOU'RE MAKING SALLY CRY!! But that's not 100% clear cut as far as reactions go, so maybe the writers thought they needed to be more obvious.
I dunno. I get what they were trying to convey so I just kind of shrugged the silly scene off, but I totally understand why it bothers some people. It is pretty silly, haha.