Okay, so back to the most common reason for not wanting the main sink in the island — dirty dishes. Look at this way: It's one way to train yourself and your family not to leave dirty dishes in the sink. If you don't want to look at the mess and the clutter, this is a useful manipulative tactic.
That said, this design may not be best for those who can't get past those habits or just don't want to. There's an ideal design out there for everyone, it's just a matter of finding the best fit.