How much goes into post production when singing?
For mainstream music, some require a lot, some require very little at all. Today's tools can correct pitch, move entrances around, shrink or lengthen phrases. Many tools in use can correct these
in line rather than in post.
But just like images, even the perfect 'out of camera' images ('studio live' is what we called them... often one of our vocalists would insist on doing the entire song that way), you touch it up in ways you couldn't or were extraordinarily difficult. You add a bit of reverb in post, maybe some analog delay, post-process compression, perhaps some eq, maybe you split-track it and play with the panning to position the audio. Like photo editing, you've an infinite amount of tools with which to screw things up, but you can also make pretty cool results as well.
Back (ages ago, we were using 24 track digital, protools and the like were in their infance) when I was cutting a guitar track on a song for a local act, I ended up doing 32 takes. They kept the first take except for the last 2 bars or so.
Many years later I was doing a bass track for a friend and we were just having a terrible time with one particular entrance. The engineer gave up on us and said 'okay, play the notes', recorded them completely out of context and moved them into place.
I've also worked with vocalists who will (need to have the engineer) piece together entire lines from different phrases.