In a FM receiver there should be a limiter. AGC is used rather to reduce limiter overload.
The AGC speed response depend on conditions the receiver is to be used (fixed, mobile), and naturally on the minimum FM modulation frequency. A faster AGC may distort the low-frequency response of the receiver.
If you drive your car in a town, you may hear the effect of multipath too. Mostly in bass response- this shows a poor AGC design, or, do not drive fast in a town!
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I find a curious detail in your "VGLNA" definition. I would not include the LNA in the AGC loop. Rather design a better limiter before FM demodulator.