Yes, the editing really destroys the sense of the entire set delivered by any one comic. So, you may like the few jokes shown from one comic, and the rest of their set may have been crap. OTOH, while you might have thought the few jokes from another comic were just OK, their full set might have been better than the comic you initially thought was funnier. And, as CBF mentioned, the producers of this show have an agenda---plus they are the editors aren't comedians.
As for the young lady from Harvard, I think everyone liked her a lot. But she was just getting started, and a bit raw. They probably didn't think she had what it took to deliver set after set, at this stage.