Thats the way people who do not know how to do it in camera will do it... not the way a knowledgeable photographer would.
Just place a light behind the subject and have it blast away at the background. In this picture we have the founder of the Montreal Strobist group posing for a shot as we were waiting for the models to arrive. From this day on, when we want to kid him and call him "tripod"... lol
Anyways, I did not use any flash for this pic, but you do see how the placement of the rear light brights and "blows out" the background so it is totally white. This is the faster and easier way to take a shot with a "seamless" background.
Of course one could do the cut and paste method, and it looks ok, but it takes more work. It does give you chances to do things that you normally could not do. This was done using your suggested cut and paste method: