Ways to focus

Short answer is no they are not.

Your focus points just find the point the camera focuses on. Center point will look in the center and try to focus on what is there.
That may not be what you want to focus on, your subject can be located in various spots of the image.

Center focus is leaned to because it is the most accurate, but using other points may be better depending on the composition, you can also half press and hold the center point then adjust the composition slightly and complete the press to capture the image. It is not perfect because the subjects new location after completing the press of the shutter is not centered and may have shifted angle / distance just a hair.

DOF - now depth of field is a math equation for the amount of the captured image that CAN be in focus.
This depends on subject distance to the camera, the fstop used and the focal length of the lens. For example you will find at f16 on a 24mm lens almost every thing appears in focus while a 200mm pointed at a subject like a bird at a distance at f4 is soft by the time it gets to the birds tail.

So ...

Getting a really good focus is very important to making sure DOF is not an issue for shorts like the bird i mentioned above.

I would say can with moving subjects trust focus tracking options and use all the focus points available.
When center point can be used it is great as it is a bit more accurate than than others.
Dial in a specific point manually if you are shooting a stationary object so you can lock in the part of the image you want most in focus.

DOF calculation in short - Wide open is in in inches, Stopped down will give you feet or yards in focus.
DOF is 1/3 in front of the focus point and 2/3 behind the plane of focus.
So lets say you focus on an eye ball and the DOF math works out to 12 inches of DOF.
4 inches in front of eye and 8 inches behind the eye.
That's plenty to not see any obvious softness if its a human, but not if its an elephant.