Pro musicians -- especially singers -- do this all the time in the studio though: there it's called "comping". Singers sing the same song multiple times, and the best takes for each part (sometimes very small moments of a few seconds) are put together to construct the best possible whole.
Somehow this is not considered cheating, but there is an ambiguity; how the performance was produced is either not known or willfully ignored by the consuming public.
Songs are like sausages. Or most things really. Better enjoy the end product and not worry about how it was made.