By now it may even be difficult for me to explain the entire depth of why subdivision based rendering and the animation of low polygon cages is the current state of the art in 3D by choice, because it has quite some amount of reasons for it’s justified success.
But let’s start at the easiest of all points:
- moving around large numbers of points may seem effortless during rendering, but in realtime performance as it is necessary during the animation process it is next to impossible to deal with. If the renderer grants itself several seconds to generate this new dense geometry for each new frame it renders, in realtime you don’t have a second between each frame, otherwise you wouldn’t be able to see the animation while you are working on it.
And some more points:
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a low polygon cage can be designed to deform correctly, by controlling just a few easily and visually separatable vertecies. When you build a setup with deformers like bones for instance, you can place them based on the visual feedback your model provides. During the smooth subdivision process for generating the dense geometry that gets eventually rendered, it interpolates between the edges of the low resolution mesh to compute a smooth surface. It still requires a little bit of experience to make use of that trade most efficiently, but this experience is easily and quickly aquired!
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The displacement possibility then allows you to fill in the vast amount of detail that such a subdivided geomtery will offers to you without interferring with your low polygon animation procedures. Some tools even allow you to animated those displacement independently from your low polygon cage and therefore allow access to this otherwise inaccessable phase to the animation during rendering.
I’m sure there are quite a whole lot more beautiful ways to mention as for why all of this, but hopeful for now that gave you an idea. I just give you one more aspect of it and that is the number of detailed objects you can deal with in one scene. Due to the subdivision principle and the ability to completely rely on the details such models can get through displacement, you can populate a scene with large amounts of them…let’s say a large group of protestors during a peace demonstration. With the right software and a proper machine it then may even be possible to animate such groups and observe them together close enough to realtime to still make judgements. Saving such a scene or better loading such a scene would only take a ridicolously small fraction of the time it were taking if you had all these models with highly detailed geometries.
Ah…if somebody else is in the mood to think about all of this again, it’s kind of fun, but I had enough of it for now… 
really great thing.