I never have a problem bagging my own groceries at the cashier. It's the best of both worlds: highly skilled checkout operator and a fairly skilled bagger.
I think the dedicated baggers they used to have were better at it than I am, though. They somehow managed to Tetris everything into appropriate bags that were of similar weight and were almost as stable as using a box.
I think the throughput of a cashier and a skilled bagger is much better than a bagging cashier and definitely better than self-checkouts.