Man, Olivia's spot on about the moving lights. That's the whole thing right there. A wrap is just a flat sheet, so the light hits it the same way every time. Real paint has grit and brush strokes that catch the light differently as the camera moves. It gives the prop a kind of life you can feel. For a quick shot it doesn't matter, but if the actor is gonna touch it or the light is gonna slide across it, that painted texture tells a better story, doesn't it?
Honestly, I read an article where a director said the camera picks up on tiny imperfections in real paint, and it adds a texture you just can't fake. That wrap might look perfect in a still shot, but under moving lights it can look flat. If the prop is a hero piece getting a close-up, that extra day might buy you some real depth. For background stuff, though, wrap all the way.