Being able to hold still and observe everything that's happening around you is the essence of bowhunting, no matter how you do it: The first step in getting close enough to a wild animal to kill it with a bow is to see or hear or smell it before it knows you're around. When you're moving, your own senses are degraded x 10 or more by your own noise and motion, and at the same time it's at least 10 x easier for the animal to see or hear you. So...
The essence of spotting game is sitting still and watching for long periods of time.
The essence of stalking game, once you get within a hundred yards or so, is choosing the least observable route from you to the game, and then moving so slowly that the game doesn't hear or see you. That often means remainin motionless for hours at a time.
Still hunting is essentially stalking game without knowing precisely where the game is located ahead of time.
Hunting from a stand - gound blind or treestand - is holding still and waiting for the game to come to you and present a shot.
Even calling involves lots of sitting still. Sure, that big bull will sometimes come crashing blindly through the timber, but much more often they either run the other way or come in quietly and nervously because they know that responding to a call, and bugling themselves, exposes them to extreme danger. I've had cougars come in to elk bugles a couple of times. Being consistently successful in calling elk (and other animals too) often requires extreme control over one's movements, albeit for shorter amounts of time.
As others have pointed out, one of the most enjoyable aspects of sitting still for long periods of time, no matter how you do it, is all the other wildlife that you would never have seen otherwise, and all the things you learn as a result.
Having said that, the degree to which you have to hold still does depend, to some extent, on the game you're hunting: If you're good enough to shoot birds on the wing or running rabbits, you may not have to hold still at all. If you know that rabbits will often sit tight if they think you're going to walk past them, and spend your time watching to the sides instead of focusing on the ones that are breaking cover ahead of you, you can move a bit more than if you try to spot and stalk the rabbits.
The bottom line is that if you ain't got the self-discipline and patience to be motionless and observant for long periods of time, you ain't gonna be a very successful bowhunter.