Implementing a sine wave inverter with an oscillation circuit
To be efficient, the output amplifier has to be switching (Class D), but other than that you're not missing anything. 

It's easier to do this with a microcontroller synthesizing the class-D drive signals directly (which become sine waves after filtering) than with an analog oscillator (which won't run at a crystal-controlled frequency without more parts, and requires AGC to get a stable low-distortion output level), so that's generally how it's done. 

I would expect you might find some very old designs (when microcontrollers and microprocessors were relatively expensive) using just that method.