Fighter engine nozzles change their shape to be most efficient at different airspeeds, primarily subsonic verses supersonic flight. Most often, when the plane is flying at subsonic speed without using afterburner, the nozzles are their most constricted. When the afterburner is applied, the nozzles expand as explained here.

For rocket engines, the traditional bell nozzle is a compromise. Instead of designing for an airspeed, rocket engine nozzles are designed to produce maximum power at a specific altitude. At any altitude higher or lower than the design altitude, efficiency drops. The higher the design altitude, the longer the nozzle.

As Tom pointed out, there have been ideas for expanding nozzles for a long time. To get around the idea altogether, the aerospike nozzle concept has been floated for many years. It was flight tested on the back of a NASA SR-71 a few years ago and was a major design element of the defunct X-33 program. While a challenge to engineer, it seems too good an idea to stay on the ground forever. If they can make it work, it seems an aerospike engine would have all the advantages you envision for a mechanically adjustable nozzle without the complexity. It might even be lighter and more efficient.