Importance of Core Work?

I have read Robertson’s article on “Core Training for Smart Folks” and others. Recently, though, I have had some questions about ab training.

So it has been said that the main purpose of the core is stabilization more than anything else and not flexion. I can understand training for stability as Robertson recommend (ie “lower ab” stabilization work for proper pelvic tilt.) However, I am not sure I see the advantage to working the obliques, TVA, Quadratus Lumborum, etc.

When you squat, deadlift, etc, your abs have to compensate, as do the other muscles in your legs, etc. You have to get as strong as is necessary to support the weight. In other words, like any other muscle, your abs get as strong as they need to be to handle the stress you put on them. I would assume, then, that they are as strong as you need them to be without directly training them.

Here’s my question: If you are NOT an athlete requiring core strength for performance and are just lifting for health, is there any real purpose is specific abdominal work other than correcting postural abnormalities?