Left Turn Arrow w/o Left Turn Lane

While driving in our nation's capital yesterday, I saw a configuration that really seemed to make no
sense.

The signal cycle began with a left green-arrow (with a red ball) for both eastbound and westbound
traffic. However, the leftmost lane was marked for Straight OR Left. As a result, if the first car
in the left lane was not turning left (which he wasn't required to do), nobody moved during the left
green-arrow cycle. Once the left green-arrow went out and the green ball came on, that first car
proceeded and the line stopped when the first car that wanted to turn left got to the intersection
and waited for oncoming traffic.

It seems like left green-arrows are almost useless when there isn't a dedicated left-turn lane.
Does this really work out somehow? Am I missing something?

P.S. I found myself in DC as part of Great Race (www.greatrace.com), a 14-day cross-country driving
event from Washington (DC) to Washington (Tacoma).