Grandmaster Joel Benjamin (see photo) answers a question on Chess Life Online about when parents should seek online lessons from a Grandmaster. Specifically, would an 8 year old rated 627 benefit? Here is part of the response.
"An eight-year-old needs most of all to establish a good rapport with an instructor. It is difficult to get to know someone without seeing them face-to-face. Your son may be reluctant to express himself to a stranger on the phone. Furthermore, you may end up with a high-rated teacher that isn’t a good match for your son."
To read the full text of Ask GM Joel, please click on the link to the USCF website. I completely agree with his opinion in this matter.