Multiple autofocusing points allow the camera to accept and input data from *multiple points* across the frame. If you have a Nikon body with the Scene Recognition System, that system uses color information (RGB color analysis) and distance information to "identify" the original subject and to follow that subject as it moves across the frame, it would be a good idea to learn how to use a grouped AF point focusing strategy for some situations. The multi-point AF focusing concept is one of the advantages of using one of the newer Nikon bodies that have color-aware and distance-aware light metering. If you had a car with five gears, would you ALWAYS use it in 3rd gear? Probably not.
Your question: is it better to change your AF points where you want the focus in the frame? is a good one; that is one way the Nikon SRS knows what target to follow across the frame; the initial lock-on,as determined by the photographer, is the way the camera knows what the original subject is; you use the multi-controller to rapidly SELECT an AF area, and then the SRS system reads the RGB values, reflectance values, and distance information,and then it can track that subject as it moves across the frame. So, yes, there is a well-known method and a known reason for the shooter selecting his/her preferred intial focusing point(s) underlying the 51-point AF system Nikon has developed.
Using just a single,center AF point in effect, is throwing away much of the capability of the autofocusing system. An AF system that can collect data from multiple locations around the frame will, if it's a newer Nikon body, be able to do better focus tracking than using *just ONE* AF location.
On the professional-level Nikon AF systems, people who encounter a lot of difficult autofocusing situations will tell you that they rely upon a multi-point AF configuration for a number of specific scenarios where using only one AF point does not produce the results they want. I would suggest some of the very comprehensive guide books, like the Thom Hogan Complete Guide to the Nikon _______ series as a way to learn more about how to use a modern, complex AF system. AF systems have become very sophisticated,and they require both understanding of the concepts AND practice to master.