Not always do I paint things over, sometimes I get it right the first time and that is the best but I have painted things over more than once or twice.
I also take failed paintings and paint over them and reuse the canvas/board for a totally different painting. All artist do this. There might be a failed painting under every success. :)
On the other hand, I never really appreciated the impressionists paintings by Monet, Van Gogh, Degas... until I saw a collection of them at the Sheaves Of Wheat show in Dallas. I was blown away by the scale and color and complete unedited enthusiasm of the brush strokes. I just had no idea! Dorm room posters and internet pictures just can not show you the wild colors, the thickness in which the layers of paint are applied and the dizzying motion that the textures create! And I'm the type of girl that usually just says things like, "Nice picture. I like that frame." Haha!
"Monet's unknown masterpiece, Dogs At Cards."
Canvases weren't a cheap commodity way back when either. Archivists have taken to x-raying paintings to reveal other works underneath them.
I much rather look at a spectaular Bierstadt than the Mona Lisa any day.