Why do we find it unnatural? If an acoustic guitar player (or singer) doesn't have dynamic control and requires compression, he's never going to be able to sit in on an acoustic jam or accompany a singer acoustically, no matter how good their pitch/bend control is.
I've done pitch correction much worse situation than simply fudging a slightly out of tune bend. I had three takes of a guitar solo we were trying to choose from. One I actually ended on a fret different than I intended, but otherwise it had more energy and drive than the others. "You're going to hate me for this, but imma use that first one and pitch shift that last note and use it". I told him I was actually in complete agreement. Why NOT use the take that most clearly makes the artistic impact we were shooting for?
Have you ever taken vocal lessons? My experience has been that at least as much time is spent focusing on each of tone, dynamic control, and projection, as on pitch. Those are hugely important parts of being a skilled singer.
Loads of singers have such bad dynamic control that engineers have to go in and clip the vocal take up into snippets and gain adjust each one BEFORE they even get to compression.
We frequently use signal processing to make up for technical limitations of performers. Folks overdo it with all of them - compression to the point the life is taken out of a vocalist's performance; EQ to the point they sound like they have ice-breath, pitch adjustment to the point that you miss the singer no longer has personality at all. But I don't see why subtle use of any of them is any better/worse than the others