Modern auto-focus systems are designed to accommodate a wide range of shooting applications that require different ways of using the auto-focus system. Which way is the best for you depends on several factors: Your subject matter, your skill level, and which setup produces the most consistent and accurate results for the particular camera/lens combination you are using.
Just because a camera includes 9/19/39/57/61 focus points doesn't mean you or anyone else should always use all of them. After all, only one distance from the camera can be in focus at any one time. What should guide your decision is to select the settings that allow you to capture the particular subject you are shooting with the most accurate and consistent (from shot-to-shot) results.
If you are shooting a static subject that is not in the middle of the frame, you might be best served by using a single focus point that falls over the part of the frame you want to be in focus when the image is already composed. If you are shooting moving targets in fast action you probably want to use multiple points with a form of AF-C/Servo focusing mode to allow your camera to track the subjects as they move about the frame.
If you are confident in you ability to act quickly and decisively and are intimately familiar with your camera's controls by touch (so that you can change settings without removing your eye from the viewfinder) you may want to use single point and control which point is active for each shot as you shoot.
In general the more you understand how your camera's focus system works and the more you learn how to control it the more you can control what the focus system locks onto instead of depending on an automatic mode that may or may not guess correctly at what you want to be in focus.
Focusing and recomposing works well for some types of photos, but not so well for others. The danger with focusing and then recomposing is that the subject distance to the lens' entrance pupil may change slightly and result in slightly missed focusing, especially when using wide apertures that result in narrow depth of field. Knowing which way and how much to move the focus ring to compensate in such a situation back in the manual focus days when most cameras were easier to focus at the center of the frame was a valuable skill gained by practice and experience.
For why the number of focus points is not as important as the accuracy/consistency of focus points please see What is the effect of the number of cross-type focus points on sharp focus?