Knowing what a tough nut KC is to crack, I'd say they were quite effective at getting her to admit to lying to them, and admitting that her lying was not helpful in finding her child.
Just my 2 cents: I agree with all of you. I also think it's really important to remember that, at that point, LE had to regard Caylee as a "missing child," so there was a tremendous urgency to get the truth out of Casey.
During those interviews with her, she stubbornly continued wasting valuable time, waltzing them around and around and around with falsehoods. So I think LE decided the quickest (and possibly only) way to make her cut out the b*llsh*t was to arrest her and toss her *ss in jail.
Understandably, they couldn't have imagined that this very pretty, petite, 22-year-old--who was foolish enough to tell them a nonsensical string of transparent lies....was actually the most formiddable, defiant, heartless opponent they'd ever encountered. She was also smart enough to lawyer-up as soon as they arrested her. Who woulda thunk it?
In hindsight, they made a mistake by arresting her, thus giving her a reason to think she needed a lawyer and causing Cindy to become LE's foe instead of an ally in the quest to find Caylee. In hindsight, LE's best chance of wearing Casey down and getting at the truth would have been to let Casey continue to live with her parents at Casa d'Crazy and keep pressuring her and questioning her constantly--possibily with Cindy present. Back then, I think Cindy might have pressured her too because Cindy so desperately wanted little Caylee brought home to her and she still believed Caylee might be alive.
Of course, that's all hindsight, as I said. Moreover all the present and former occupants of Casa d'Crazy seem to have experienced some sort of brain decay that causes them to be irrational, unpredictable, mean, rude, and dishonest. Oh, wait--most of those are character flaws, aren't they. Well either way, some environmental agency needs to immediately check Casa Crazy's surrounding soil and water supply.
IMHO