If you remove the diodes then the output will increase until the output of the opamp clips.
There are many high frequency oscillators that use tuned LC circuits to make a sine-wave. I think some oscillators with a quartz crystal have a sine-wave.
I made a low distortion sine-wave oscillator as a phase-shift type.
A resistor in series then a capacitor to ground creates a lowpass filter with a 60 degrees phase shift. It is buffered with an opamp then feeds another and another to make a total of 180 degrees phase shift. The last one is buffered and is the low distortion output which is inverted by a 4th opamp that clips and feeds the input.
The 3 lowpass stages reduce the clipping distortion to nearly nothing.
The lowpass filters have a little amount of loss that can be made up if the opamps have a little gain.