I want to repaint the baseboards in rooms where the original hardwood was covered by carpet. Now that the floors are beautifully refinished, the paint/stain lines really show, and the occasional carpet glue & fuzz adds an unwanted texture.

Is it better to cover the floor and sand/repaint baseboard in place? Or should I remove them, sand/paint, and then reinstall?

FYI, the baseboards are real wood (house dates from late 1950's), and the company that we hired to install hardwood in two areas made it look super easy to remove & replace them. Of course, they are professionals!