There are schemes that remove the old vertices at each step, but they re in the definite minority. Topology is a way of describing the structure of a surface that isn t changed by an elastic deformation, that is, a stretching or twisting. A good example and common joke is that to a topologist, a coffee cup and a donut are identical. The donut hole corresponds to the hole in the handle of the coffee mug. On the other hand, a sphere and coffee mug are not topologically equivalent, since no amount of stretching and twisting can punch a hole in that sphere.
Topology is one reason that subdivision surfaces are worth a look.
With B zier or B-spline patches, modeling complex surfaces amounts to trying to cover them with pieces of rectangular cloth. Furthermore, trying to animate that object can make continuity very difficult, and if you re not very careful, your model will show creases and artifacts near patch seams. That s where subdivision surfaces come in. On top of that, since the mesh produces a single surface, you can animate the control net without worrying about seams or other continuity issues. As far as actual uses in games, I believe that subdivision surfaces are an ideal solution for character modeling.