Live games are filled with mistakes. I wouldn't recommend it even if it was possible
My Live Chess Games Database

Also, because I play a lot of live games I could do a stastitical check on what openings I do well in

I don't follow the logic that if live chess games are full of mistakes then there's less of a reason to view them in a game explorer type tree. Chess games played over the board are filled with mistakes. Tal built a career on playing what later turned out to be questionable moves. The benefit to the player would be the same: to objectively see what kind of tendencies you have in games.
So I also would love to see the game explorer feature for live chess games.
I've noticed that in the Game Explorer I can look search my online chess games in the database but not my Live games. Since I primarily play live chess this is a bit of a downer. Any chance of getting live games added to the database?