I've been using a handlebar bag that opens towards the rider for about a year now (home-made version) and while it's not ideal, I haven't really found it to be much of a problem to use while riding. Even with the bag sitting several inches below the handlebar, I can still reach in and pull out just about anything I need without to much trouble.

If I were designing a bag from scratch (again) I would do it differently, but the hassle is not nearly enough to make me go through the effort again, or even to dismiss an otherwise well built bag.