The question is: how does getting your child into the school then moving serve as an advantage to you, the parent? A small minority might do it for selfish reasons (such as reducing their housing costs), but moving is expensive and disruptive, and having to travel to get your kids to school really affects the family's quality of life. Having two kids at one school far from where you live is not much better than having one close and one not.

Moving if you don't have to is going to make your life more difficult, not less, so I don't see how this counts as rigging the system.