I wouldn't assume there's an overall efficiency gain. That's part of the problem: in many cases, a shortcut that would work if a few cars used it causes problems (jammed intersections, etc.) if too many cars try to take advantage.
Someone who knows graph theory more than I do could comment, but more generally I don't think there's any guarantee that a situation where every vehicle uses a greedy algorithm will result in overall greatest efficiency. I could swear there was an article on this within the last year but I cannot find it.
At least in the UK, in a lot of cases that's just not feasible. Take the image I posted above for instance: http://c8.alamy.com/comp/DXHF2G/terraced-street-in-hillsboro...
The only ways to widen the road would be A) prohibit parking -> now residents have nowhere to park, or B) start demolishing houses.
Maybe it is also in your best interests if the street is modified to accommodate modern use cases.