My take would be, first off, that Georgiou's never seemed like the type to delegate, and second, that I think she set this as a trap for Burnham. She knows something's up, and she demanded Burnham do this as a test, suspecting that Burnham would fail it.

It is a little bit dodgy mostly because this is supposedly an emperor no one has seen in person... but that always stood out as an obvious plot contrivance to delay the reveal of Georgiou until it was a face-to-face.