I agree, except for the fact that the AGC loop will take a long time to settle when the frequency is low. Direct digital synthesis is the clean way to do it, but is more complex. A function generator with a sine shaper , e.g., XR2206 is another way. Still another method uses a switched capacitor filter.Even though the mulivibrator section can be varied in frequency as AudioGuru said, the filters which are intended to make puesdo sine wave are fix-tuned to one specific frequency, and will not work over three decades. If you need a sine waves, you should be looking at an intrinsically sine-wave oscillator, like a Wien-Bridge.
Two polarized electrolytic capacitors in series and back-to-back make a non-polarized capacitor with half the value of one.
Your extremely old and simple circuit makes a poor sine-wave with a single frequency. You might make it switch parts for other frequencies. Three capacitors and/or three resistors must be changed at the same time.
The 741 opamp is too old and slow to make high frequencies.
Very true Brownout, if the sine wave source is the entire project.
But I suspect it is just one building block of something far larger.
While it is entirely possible to build your own op amps and +5v regulators out of discrete transistors, and learn much in the process.
There comes a point where a quad op amp or 7805 saves a lot of time board space and money.