One of the insiders, maybe Shelley, pointed out that What's on the show is a tiny percentage of what really goes on. K & J are apparently there just during filming and most rehearsals are run by GL and assistant choreographers. If Jennifer was asked for input it's likely because she'd seen the girls practice. It seems unlikely that was Lily's first notice there was anything wrong. Tara was the only one that actually seemed surprised by her cut.
As far as dragging out TC, they have so much to learn that a couple months seems reasonable. Even though the drama is in the cuts, the majority of it is probably learning and practicing dances as well as learning the practicalities of being on the team such as how to behave at appearances.