"Sometimes reading glasses and a good slouch isn't enough to detour people. They see. As invisible as you might feel when you're not wearing a cape, some people still see what you're capable of. I guess I should find that touching, but..."
It complicates things. And Kat was so wrapped up in how much the city needed her that she was going to make her choose between her job and being Supergirl. Kara needed her job. Sure, she could've easily got herself put on the DEO's payroll, but that wasn't how this was supposed to work. She was supposed to be able to have a normal personal life beyond the call of super duty.