I don't say this will work for every papered wall, but my painter redid a wallpapered kitchen by applying a coat of good quality primer right over the wallpaper to eliminate any sight of the pattern (dark green ivy vines on white background). Now it looked like a solid, primed wall. Then he painted the color I had selected and painted over the primer. Voila! Freshly painted room with no wallpaper removal hassle.
It's been like that for several years. My kitchen is a dove gray with white trim and white cabinets. The wallpaper stayed on the walls, the paint color is still there and labor was vastly saved.
It worked well enough to convince me to do the same on the bathroom walls above the lower tile. It's a small bathroom and I did it myself. I primed it and painted it by myself one weekend. Very satisfying and worth the couple of hours for the primer and main paint to go on a day apart.