For what it's worth, I moved several times during my childhood (my father was a diplomat, so it was to different countries, not just different states) and frankly I loved it.

As you say, each location is a new start, a break from earlier expectations, and a chance to reinvent yourself. I strongly feel the benefits outweighed any negatives.

I am friends with some folks who have lived in a single area their entire lives, and while they do have a feeling of 'roots' that I will never have, they also have a smaller worldview. Not their fault, in the sense that you can't expect someone who hasn't experienced something to understand it, but I'm glad I lived the life I did.