Using +10 dB of preamp gain all the time will result in lower dynamic range and better sensitivity. However, if the band noise is high enough, which with a full size antenna will almost always be the case on 20m and below, using a preamp will result in no improvement in sensitivity, but will always result in lower dynamic range, which might be a problem if there are large signals present.
A side-affect of using too much preamp gain will be a noisier recovered audio signal. Which is your complaint.
An SDR is no different in this regard than any other topology. If you simply crank the RF gain up, the AGC will likely wind up acting on it. That is why receivers have RF gain controls, and we have a preamp capable of attenuation, or gain.
In the Anan, if you research it, you will find the best receiver performance (dynamic range) will occur if you apply S-ATT to each of the lower bands.
To determine if preamp gain is needed is easy, simply turn off any auto AGC, switch between your receive antenna and a dummy load (or another input port). If the band noise is substantially higher with the antenna connected, keep lowering the preamp gain until you have perhaps 10 dB of excess band noise over the no-antenna case. Then you will have little sensitivity degradation, and maximum dynamic range. You'll also have better (lower noise) recovered audio.
Try what I suggest as an experimentation to set the preamp, and then see what you think about ANC with the auto gain set to at least 15 dB. Go back and forth with the Anan and NR2. I have many times. The Anan is better, but the Sun is not bad.
Just my two or three cents ...
Doug