People clamour for exercises. It's no good in a martial art telling folk it's all about stance- they want exercises. So they get them. Exercises exist to build awareness. The exerise may look like something else- an attack, a punch, a throw- and it may 'work'- but it exists to build awareness- so that you may become your own teacher. A teacher is someone who helps build awareness. They direct you to activities that shift you up the neural ladder- by this I mean you become aware of greater subtleties, broader connections. When you become your own teacher- you already are- this is more about a shift in emphasis, in dependency, you actively seek out that which increases awareness. You might even invent your own exercises.
In many mystical traditions they also have exercises. These have several functions including providing a teaching matrix in a culture which outlaws the verbal expression of certain ideas. But if people get verbal about exercises they miss the chance it offers- to build awareness. You can also easily become obsessed by certain exercises- yoga offers plenty of examples of that. Because the body and mind are so interlinked physical exercises are a convenient way of shifting one's attention. Becoming aware of this, of both the body and the mind and the ability to shift attention, is the important thing- not the mental 'experience' of calm or feeling good. Talk of centres is a way of shifting attention and building awareness. Centres tend to coincide with places with the most nerve endings - making the acquisition of subtler circuitry easier- but you could have a centre in your big toe if you wanted.