Would putting several small propellers on a wing be efficient? I saw this video that NASA posted, which presents the idea of putting several small propellers on a wing:



They claim that by doing this you can force air to blow over the wing more quickly. This would make the wings act as if the aircraft was flying faster than it really was, resulting in shorter takeoffs and more control on landings.

However while watching the video I kept thinking, wouldn't the turbulence and slipstreams caused by the propellers actually make the wings perform worse? Or at least neutralize the proposed added lift and control?

Having no fresh airflow over the wings seems like a problem. Have any aircraft ever tried this concept before with successful results?
It would provide pretty good STOL performance at low speed because there is a significant increase in lift with the wing in the slipstream of a propeller, especially with flaps down.  One of the biggest differences between a jet and a turboprop while flying a landing approach is that power settings have a direct effect on sink rate with a turboprop where a quarter or a third of the wing span is in the propeller slipstream; not so much on a jet.

Then when you speed up, the inefficiency of all those draggy nacelles and relatively inefficient smaller propellers, the weight, the maintenance nightmare, the fuel burn.  Yikes.  That's why it's not done.

There's a reason that airplanes are all built to a few near-universal configurations.  They are the arrangements that hit a sweet spot, in the balance of compromises game, for the airplane's mission, and they are timeless until some major new paradigm comes along.  That's not one of them.