Often the simplest of things are revealed as complex. As Jerry says, the delays are important. The values used allows the attenuation to smoothly increase and track the signal level variations such that the response is fast enough to produce a pleasant result but not so fast that it will oscillate. Your confusion may be that you perceive that the end result is a tightly controlled output. It is not. Stronger signals result in slightly stronger audio levels. A S9+40 dB signal will be a bit louder than a S9 signal, just not horribly so. That increase is designed to be slight and gradual. This simple circuit is almost (but not quite) linear in that respect. Fortuitously, the shunt resistance takes over as the series resistance nears maximum conduction and it is a nice, gentle, transition. Close but not perfect. Good enough.
To get a better AGC, especially one that tames the initial burst, you would need a much more complex circuit. The better ones include an additional detector and multiple additional gain control points throughout the RF and IF amplifiers. If we had a carrier to use as a signal strength reference then it would be easier. Without the carrier we have to rely on the modulated signal. Tricky.
I use a compromise circuit. Even then, it seems that it is so complex that the majority of builders need kits or completed boards. This circuit is the best that I can do (so far) in keeping it simple yet effective.
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