I record lots of classical piano, with a superb pianist, and when we first started, he'd play the entire piece in one go. Maybe 3-5 minutes, that's all. He'd make a tiny mistake, and play the whole thing again. Often curing the first fault but making a new one. My the fourth take the mistakes increase and in the end, we'd give up, and sometimes, the released track would have a tiny mistake in it. Often, only serious pianists with a good knowledge of the work would ever notice. Then I suggested a new process. The form of the music might be ABA, for example so why not record the first section, and then stop. Do it again if there is a mistake, but if not, then move on. It took far less time to stitch these back together in the studio afterwards, and the result is a much better recording. There's a difference from producing a good recording from an inept player by editing, and doing the same thing with a skilled player. However, as it's private, and nobody really knows, does it matter to anyone other than those present. My pianist colleague gets very stressed when he makes mistakes and it comes through in the music. I've now introduced him to the concept of recording on a master keyboard and then using a VSTi of the same piano as he has. At first he wasn't sure, but the delicacy of editing he's now using as a tool. We play a phrase, he thinks it's not quite right - we look at it on screen and he can 'see' the slightly too short Ab, and we can stretch it. He is now a convert. Sound wise, he cannot tell the difference between his umpteen thousand pounds worth of grand piano and the VSTi. I can, and although his piano sounds slightly better to my ears, his room doesn't - and the acoustics in the sample are better.
So in my humble view, editing is improving musicianship - just afterwards, not during!
...so I guess I would never hear that 111th "perfect" take. 
