I use different methods for different players. Sometimes you can tell right off the bat as you rehearse a take that the player or the singer has something blocking their ability to settle into their part. For whatever reason. The function of Producer is to identify this and remedy if so. A modern full-function DAW makes it really easy to comp a complete performance from a list of takes. This is MUCH easier with guitars, bass, solo electric instruments in general, since the sound is sort of set. If your'e doing takes and experimenting with different sounds, tunings, neck positions, amps, guitars etc, then you're arranging more than looking to comp something. In a virtual track world it doesn't make any sense NOT to red light everything.
Vocalists are different. Personally, I am looking for a take that tells the story of the song and does it with the mood, energy, and basic accuracy of the melody while feeding the listener with the lyric. Vocalists are somewhat harder to comp through multiple takes simply because, (and this isn't ALWAYS TRUE, )the voice will change as the session progresses.....the position on the mic changes....even slight changes can make an audible difference in tonality......the feel exuded by the singer changes as their emotional attachment or DEtachment changes towards the work. I'm lucky in that I have a room I can crank open the mic chain without any noise and let the vocalist set their hair on fire if that's what it takes to get the "magic"... Some singers like the intimacy of a close-micd take and having a really good headphone mix allows this to work in their favor.
But the bottom line is getting the emotional content coupled with accuracy with the energy the song calls for in it's natural content. Sometimes this means turning all the lights off and bringing in a stage light or two.
I usually coach a singer through takes. Sometimes the words say the right thing but don't sound good in a sentence. Or don't have a way to meter into what the music is asking for. Making it all match is the whole point.....isn't it?