A question about the Supergirl T.V series finale......

This question is directed toward those who followed the Supergirl T.V show and who have watched the series finale.The series ends with Cat Grant taking over her old media empire and hiring Kara as her editor-in-cheif.In the final scene,there is an interview with Kara as her reveals her secret indenity to the world.It is implied that she intends to balance her public and private persona with everyone knowing who she really is.Thats all fine,but there's a problem that nobody's been talking about:wouldn't doing that endanger Clark Kent's indenity as Superman?On the show Cat Grant figured out who Supergirl was on her own.On the show,Grant has met and even had a crush on the T.V version of Kent,who had appeared on the Supergirl show.On the show,Clark as introduced as Kara's cousin.They both wore glasses,were reporters and has that navie,mild-mannered personality.Would it really be hard for Cat Grant to put two and two together?And by extension,wouldn't the world quickly figure it out?