Why does input attenuation reduce receiver overload on the lower frequency HF bands with little or no impact on signal-to-noise ratio?
Why On 160, 80 and 40 meters the noise you hear is external: atmospheric static, lightning, and man-made noise arriving through the antenna. That external noise is typically far stronger than the receiver's own internally generated noise, so inserting 10 or 20 dB of attenuation knocks down signal and band noise together and the signal-to-noise ratio stays essentially the same, while the reduced total power keeps the front end out of compression and away from intermod. Attenuation only starts hurting SNR when the band noise drops close to the receiver's own noise floor, which is typically the case only at VHF and above or on very quiet high bands.
Watch out The idea that signals are attenuated separately from the noise is wrong because a pad is a simple broadband resistive network, it cannot distinguish signal from noise and reduces both by the same number of dB. There is no filter of any kind in a plain attenuator.
Low HF: the band is noisier than the radio, so pad both down equally and SNR doesn't change, but overload does.