In my mind, obstacle commitment is closely related to "trust", "finding the line" and "proofing" obstacles. The biggest reason to work on and perfect obstacle commitment for me is so I can get to where I need to be ON TIME! The other very compelling reasons are that the dog is able to execute the course in a fluent and fast manner. Fluent = easier on their body = faster times.
What is obstacle commitment to me? The moment the dog sees the obstacle. Not the moment it can no longer take another obstacle, nor the take off point of a jump, or many other popular definitions. If it is the moment the dog sees the obstacle, then it is my job to show the dog the correct line so that it sees the intended obstacle (then I need to be there to show them the correct line, kind of circular thinking).
Once I have the dog on the correct line, cued the obstacle I need to be free to get out of there and get to the next place I need to be. Easier said then done sometimes. If I haven't taught my dog to stay committed to the obstacle, then I am stuck somewhat escorting the dog on their path. Not what I want to do.
Consider the black circle sequence. If I can't cue the weaves and then feel free to move laterally (because my dog doesn't stay committed) then I run a real risk of not being able to set the line to the backside of #2. There is an off course jump on the dog's line. This also illustrates why it is so closely related to proofing and trust. Have you proofed your dog to stay in the weaves under many adverse conditions (you doing cart wheels for instance?). Can you trust that your dog will stay in the weaves?
In the black square sequence, there are two places that I need commitment and for them to stay committed to the obstacle. Say #1 is mid-course. I need to be able to cue the backside of #2 from about 1/2 way in between 1 & 2, then move laterally to #3 to show the dog the backside. Even more commitment is needed if I intend on doing a German turn on #3 for instance. To do a lateral send takes proofing your dog's backside commitment at a distance.
OK, let's talk young, very green dogs for a moment. The first time I did a pin wheel with Hoot I had to go all the way in to the middle jump of a pin wheel. Not too uncommon. Eventually, with experience most dogs learn to take that middle jump without you going in to it. Perfect example of commitment.
Selfishly speaking, the reason I teach commitment and to stay committed is so that I can run with less panic, more trust, less wear-n-tear on my dog's body, and more confidence in my ability to get places. The faster times don't hurt either :)