A perfect example is when I set up lighting and had my client posing in the light, there was a frame I loved, but I didn't like her hand. It looked awkward and claw-like to me. But, when I directed her to soften her hand position, and I repositioned myself, we lost the moment.
However, even though the moment in the first image is more authentic, the hand "claw" ruins it.
This second image is better posed, the expression is still good, but it's not as unguarded as the first one. The second image with the softer hand is more pleasing.
There must be a happy medium where you can let go perfectionism to create authenticity, but you still need to be aware of distractions and unflattering poses and camera angles.