In most cases, prerecording should be a mixed bag. It is a clear advantage for people who are at both extremes of skill and experience, and basically a wash for those in the middle.Seems like there would be a big advantage to being prerecorded, then, especially in the "doesn't always get the timing" age groups and proficiency categories. I also remember being impressed with Jennifer Lopez' dancing in Shall We Dance 2004 until I watched an uncut video of her doing several takes, where she was falling off her feet in a majority of takes.
I say this because of my experience recording video and radio. Putting an amateur in front of a camera or microphone in an empty room yields a peculiar response: they experience all the psychological stress of performance, but feel none of the positive energy of being in front of a crowd. The results can be shocking! Folks who normally have no stage anxiety whatsoever seem to entirely lose their minds. So while they do have the option to only keep the cleanest take, the energy level and performance quality suffer compared to a good day performing live.
On the extremes, though, you're right--prerecording is unequivocally great. On the unskilled side, you have J-Lo's example: avoiding negative variance by keeping the one take that wasn't horribly flawed. On the skilled side, you have folks who are able to bring high-octane performance energy under any circumstances, so the opportunity to keep only the best take has no associated downside.
Also worth mentioning: the upsides of recording only appear when you set a side *a lot* of time to do it. I'm talking 10:1 or more. I image most folks won't do that.