Ok hear me out! I came up with a theory about Kara's not so good disguise :

What if the fact that those glasses and ponytail works is only because almost no-one in her close entourage actually wears glasses. Like there's Cat, who has known for I don't know how long, there's Lillian (I'm 90% sure of it but I can't seem to find any proof on Google and I'm not willing to rewatch the whole show just to find a scene with Lillian wearing glasses), who knows since their first interaction or so, there's Snapper, who, lets be honest, doesn't give a fuck, and there's Clark, obviously.

As far as I remember, the only other one who knows Kara's identity without being told about is Lex. And I don't know if he knew all along or if he found out with the CCTV from Kasnia. So let's say that he either found out not before telling Lena or Lillian told him.

As a regular glasses user I can tell that a lot of people struggle to recognise you without them on. The only exception I know is other glasses users themselves. Indeed, I never had any difficulty recognising people usually wearing glasses without them on.

Therefore, it only works because they (the people in close contact with both Kara and Supergirl) are not used to seeing people wearing glasses without them on.